ARPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces
AARPES Studies of Two-Dimensional ElectronGases at Transition Metal Oxide Surfaces
Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger
Abstract
High mobility two-dimensional electron gases (2DEGs) underpin today’ssilicon based devices and are of fundamental importance for the emerging field ofoxide electronics. Such 2DEGs are usually created by engineering band offsets andcharge transfer at heterointerfaces. However, in 2011 it was shown that highly itiner-ant 2DEGs can also be induced at bare surfaces of different transition metal oxideswhere they are far more accessible to high resolution angle resolved photoemission(ARPES) experiments. Here we review work from this nascent field which has led toa systematic understanding of the subband structure arising from quantum confine-ment of highly anisotropic transition metal d -states along different crystallographicdirections. We further discuss the role of different surface preparations and the ori-gin of surface 2DEGs, the understanding of which has permitted control over 2DEGcarrier densities. Finally, we discuss signatures of strong many-body interactionsand how spectroscopic data from surface 2DEGs may be related to the transportproperties of interface 2DEGs in the same host materials. Siobhan McKeown WalkerUniversity of Geneva, 24 Quai Ernest-Ansermet, Geneva, CH-1211, Switzerland e-mail: [email protected]
Flavio Y. BrunoUniversity of Geneva, 24 Quai Ernest-Ansermet, Geneva, CH-1211, Switzerland e-mail: [email protected]
Felix BaumbergerUniversity of Geneva, 24 Quai Ernest-Ansermet, Geneva, CH-1211, Switzerland and Swiss LightSource, Paul Scherrer Institut, Villigen, CH-5232, Switzerland e-mail: [email protected] a r X i v : . [ c ond - m a t . s t r- e l ] D ec Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger
Oxide surfaces and interfaces can host electronic states that differ from those in thebulk. This offers new possibilities for electronic structure design and has motivatedan increasing number of studies investigating epitaxial heterostructures. The ABO perovskite transition metal oxides (TMOs) have received much attention in this con-text because their quasi-cubic structures and compatible lattice constants make themwell suited to heteroepitaxy growth [116]. Moreover, they show diverse bulk proper-ties including ferro- and antiferromagnetism, ferroelectricity or superconductivity.These phases are largely controlled by the occupation of the transition metal d -shelland by subtle changes in bond angles, rendering ABO TMOs suitable to electronicstructure engineering in heterostructures by exploiting interfacial charge transfer,strain and octahedral tilting patterns [96, 59, 116].Of particular interest are high-mobility two-dimensional electron gases (2DEGs)in ABO perovskites. These systems have the potential to underpin a new gener-ation of oxide electronics by exploiting not only the various phases of the par-ent oxide as carrier densities are tuned, but also phases and properties unique tothe oxide surface or interface 2DEG [59, 41]. Determining the intricacies of theelectronic band structure of such TMO 2DEGs is an important step towards under-standing the underlying physics of these systems and facilitates the engineering ofdesirable properties. However, the intrinsically buried nature of interface 2DEGsposes substantial experimental challenges. High-resolution angle resolved photoe-mission (ARPES) using UV excitation, a standard technique for band structure de-termination, has insufficient probing depth to study important systems such as theLaAlO /SrTiO (LAO/STO) interface 2DEG, despite them being buried beneathonly a few unit cells. This restricts photoemission studies of interface 2DEGs to thesoft or hard X-ray regime where the effective resolution in energy and momentum isreduced. Other spectroscopic techniques that were successfully applied to oxide in-terfaces such as X-ray absorption (XAS) [84] or resonant inelastic X-ray scattering(RIXS) [7, 114] give valuable information on orbital symmetries and collective ex-citations but do not offer direct momentum space resolution. Microscopic electronicstructure information from interfaces has also been deduced from quantum oscilla-tion data. This technique is exceptionally precise but requires very high mobilities,which are hard to achieve in correlated electron systems, and the data is often dif-ficult to interpret [31, 70, 60, 44]. These challenges have motivated an alternativeapproach to the creation and spectroscopic investigation of oxide 2DEGs. Recog-nizing that the fundamental electronic properties of 2DEGs are defined by their hostmaterial and the electrostatic boundary conditions, in 2011 Meevasana et al. [65]and Santander-Syro et al. [86] reported that a 2DEG showing hallmarks of the bandstructure predicted for the LAO/STO interface can be created on the bare (001) sur-face of SrTiO (STO) where it is accessible to high-resolution ARPES experiments.This approach has subsequently been extended to different TMO host materials andsurface orientations revealing the fundamental electronic properties of oxide 2DEGsand a common framework for describing system-to-system variation. In this chapter,we review the present status of this emerging field. RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 3
We will focus the discussion on ARPES studies of 2DEGs with d orbital characterin the transition metal oxides SrTiO [86, 65], KTaO (KTO) [48, 85, 5] and anataseTiO [71, 81]. We note that electron accumulation layers have also been observed onthe surface of the transparent conducting oxides CdO [76, 51] and In O [111] butthese 2DEGs derive from free-electron like s states and will not be discussed here.In stoichiometric form, STO, KTO and anatase TiO are band insulators with a d configuration of the transition metal ion. Importantly, all three materials are suscep-tible to chemical doping [90, 93, 106, 98, 32, 40] which introduces electrons intothe conduction band minimum resulting in a three dimensional bulk metallic state.Using appropriate surface preparations, electron accumulation layers that are inde-pendent of the residual bulk doping have been reported in all three of these TMOs.As shown in Fig. 1, these charge accumulation layers all show multiple subbands,which is a key-signature of quantum confinement and is adopted as the finger-printof a 2DEG in ARPES measurements throughout this review. In the following we willdiscuss the subband structures of 2DEGs in STO, KTO and anatase TiO in detail,exploring not only material dependent electronic properties, but also the influenceof the crystallographic orientation of the surface on 2DEG characteristics. We willfurther discuss the origin of these metallic states on the surfaces of insulating TMOsand briefly review different approaches for calculating their band structure. We willalso summarize very recent ARPES studies that provide insight into the nature ofmany-body interactions in oxide 2DEGs. E – E F ( e V ) || ( Å -1 ) k || ( Å -1 )k || ( Å -1 ) b ca Fig. 1
Energy-momentum dispersions of surface 2DEGs measured by VUV ARPES on the (001)surfaces of (a) SrTiO , (b) KTaO and (c) anatase TiO . High intensity (black, black and whitein (a), (b) and (c) respectively) delineates the electronic states of the charge accumulation layer.Adapted from Santander-Syro et al. [86], King et al. [48] and R¨odel et al. [81] respectively. Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger A 2DEG arises as the conduction band minimum of an insulation or semiconductingcrystal is dragged below the chemical potential by an electrostatic potential over anarrow region. Understanding the origin of the corresponding electric field in 2DEGsystems is an important step towards achieving carrier density control, which in-turnunderlies device functionality. While in conventional semiconductors it is well es-tablished that the potential gradient arises from workfunction mis-match, the originof both the attractive confining potential and the excess charge carriers in TMO sur-face and interface systems is more ambiguous. For example the origin of the nativecharge carriers at the LAO/STO interface is still actively debated and consequentlysystematic control of their density has remained elusive.The first two publications that reported the STO (001) surface 2DEG, suggestedthat the origin of both the electrostatic band bending and charge carriers may besurface oxygen vacancies (OVs) [86, 65]. In this scenario two excess electrons arereleased as a positively charged OV is created. This positive charge at the STOsurface must be screened by the excess electrons which can form either localizedstates near the vacancy, or an itinerant accumulation layer which manifests as theobserved 2DEG. Additionally the authors of reference [65] observed that the 2DEGbandwidth and density increase as the surface is irradiated with synchrotron lightand remains constant in UHV conditions when not irradiated, leading to the hypoth-esis that the STO surface 2DEG originates from light-induced oxygen vacancies. Inthe following we will describe the experimental evidence for this scenario.
Both Santander-Syro et al. [86] and Meevasana et al. [65] saw evidence for bandbending at the (001) STO surface. They measured angle integrated energy distri-bution curves (EDCs), similar to those in Fig. 2(a) which shows the O2 p valenceband (VB) whose maximum is around 4 eV below the Fermi level before signif-icant irradiation (blue), after long UV irradiation (red) and at intermediate times(grey). Its can be seen that the VB appears to shift to higher binding energies asthe surface is irradiated. Together with small core level shifts observed by X-rayphotoemission spectroscopy (XPS) [26, 77] this suggests the presence of downwardband-bending at the surface induced by the UV radiation [65, 62, 63, 26]. This bandbending appears concomitant with the 2DEG peak at the Fermi level (see inset) andits magnitude, which can be broadly quantified by the shift of the VB leading edgemid-point, should be related to the 2DEG bandwidth. However, the exact magnitudeof the surface band bending is difficult to extract from such spectra since they repre-sent an average of the energy shift in each unit cell over the photoemission probingdepth, and the form of the VB also evolves as the surface is irradiated.In addition references [86] and [65] observed a non-dispersive in-gap (IG) stateapproximately 1.3 eV below the Fermi level that grows in intensity with increasing RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 5
475 470 465 460 455Binding Energy (eV) pristine irradiated irradiated + O Ti 2p I n t e n s i t y ( a r b . un i t s ) I n t e n s i t y ( a r b . un i t s ) -6 -5 -4 -3 -2 -1 0E - E F (eV) ba Fig. 2 (a) Angle integrated energy distribution curves showing the valence band, in-gap state and2DEG evolution on the fractured surface of La:STO (001) after negligible (blue) or prolonged(red) UV irradiation and for intermediate irradiation times (gray) (unpublished). (b) XPS showingthe Ti + core level under the same conditions and after exposure to 0.5 Langmuir of O (green),adapted from McKeown Walker et al. [62]. irradiation time (see inset of Fig. 2(a)). Previous photoemission measurements onreduced STO, Nb:STO and La:STO also observed this IG state at the STO surfaceand associated it with oxygen vacancy defects states [36, 1]. Further evidence thatelectrons localized on or near oxygen vacancy sites would form such an IG statewas provided by DFT calculations of STO with oxygen deficient surfaces [42]. -0.4-0.20.0 E - E F / e V -0.3 0.0 0.3k || /Å -1 -8 -4 0E - E F /eV -0.3 0.0 0.3k || /Å -1 -0.3 0.0 0.3k || /Å -1 I n t e n s i t y / a r b . un i t s -8 -4 0E - E F /eV -2 0 -8 -4 0E - E F /eV -2 0-2 0 -4.20-4.10 V B L E M / e V D E G b a n d w i d t h / m e V (a),(d) (b),(e) (c),(f)(a) (b) (c)(d) (e) (f)(g) Fig. 3
Creation and annihilationof the 2DEG at the STO(001) surface. (a) Dispersion plot of thehigh density STO(001) surface 2DEG after initial irradiation with 52 eV photons. (b,c) The 2DEGdisappears after in-situ exposure to 0.5 Langmuir of O and reappears following further irradiationwith 52 eV photons. (d-f) Angle integrated valence band spectra corresponding to the states in(a-c). The magnified insets show the intensity at the Fermi level. The valence band leading edgemidpoint (VB LEM) is marked by a cross. All data were measured in the second Brillouin zonewith 28 eV, s − polarized light. From McKeown Walker et al. [62]. Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger McKeown Walker et al. [62] demonstrated that, as shown in Fig. 3(a)-(c), intro-ducing extremely low doses of molecular oxygen into the UHV chamber eliminatesthe surface 2DEG and that subsequent irradiation with UV light causes the 2DEGdensity to recover. This explicitly demonstrated that the 2DEG is an accumulationlayer of electrons at the surface of STO screening positive charge resulting fromlight induced oxygen vacancies. This experiment also confirmed that the IG state isassociated with light-induced OVs providing evidence that these defects at the STOsurface result in both itinerant and localized electronic states. Reference [62] alsodemonstrate that the efficiency with which OV are created depends on the photonenergy, suggesting that the dominant mechanism by which OV are created is inter-atomic core-hole Auger decay [54, 53]. Using this knowledge McKeown Walker etal. succeeded in controlling the density of the STO 2DEG by either measuring ata photon energy below the threshold for efficient OV creation or by measuring athigher photon energies while maintaining a partial pressure of oxygen during themeasurement.The bandwidth and density of the STO surface 2DEG do not grow indefinitelyunder synchrotron radiation. After a finite irradiation period the band width satu-rates. However, as reported by Dudy et al. [26] the intensity of both the IG stateand 2DEG do not saturate over the same time scale. These authors suggest that thedynamic equilibrium between OV creation and annihilation at finite oxygen partialpressure leads to OV clusters and electronic phase separation. Alternative explana-tions include the migration of ions within the lattice due to high electric fields at thesurface, and that the ratio of localized and itinerant electrons donated by an oxy-gen vacancy evolves as a function of OV density due to a changes in the balance ofcorrelations [58].Qualitatively the same UV sensitive behaviour of the two-dimensional electrongas density, VB and core level shifts and IG state intensity has been observed forvarious low-index surfaces of STO [63, 104, 80] and for the surface of anatase TiO [81]. The carrier density of states observed by ARPES at the surface of anatase TiO could be controlled by tuning the dynamic equilibrium between OV creation by UVlight and re-oxidation due to finite oxygen partial pressure in the chamber [71].Indeed the role of oxygen vacancies in TiO thin films is even more dramatic withexcessive irradiation leading to a local destruction of the 2DEG state [81]. Implicitin these observations is that reconstructions of the crystal surfaces [77, 17, 20] donot dominate surface charge accumulation in STO or TiO . This is true even in thecase of (111) and (110) surfaces of STO which are polar. On the other hand, for the2DEG at the strongly polar (001) surface of KTaO only a weak evolution of the2DEG bandwidth is seen as the surface is irradiated [48, 85], suggesting that defectsintrinsic to the cleaved surface may induce a 2DE in this case. RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 7 In this section we will describe the subband structures of STO 2DEGs observed byARPES in more detail. We will demonstrate that the characteristic features of theelectronic structure can be understood on a qualitative level in terms of quantumconfinement thereby justifying the identification of these states as two dimensionalelectron gases. We will also discuss the role of crystallographic orientation of thesurface in modulating the effects of quantum confinement on the 2DEG band struc-ture. (001) Fig. 4(a) shows the energy-momentum subband dispersion of the 2DEG measuredon the fractured (001) surface of STO. This data, reproduced from reference [62],resolves five subbands, as shown schematically in Fig. 4(b). Three subbands (L1-L3) are highly dispersive indicating a light effective mass for some of the carrierswhile the two shallowest subbands (H1-H2) resolved in the experiment are muchless dispersive. From parabolic fits of the overall dispersion of individual subbandswe estimate effective masses of ∼ . m e for L1-L3 and 9 − m e for (H1-H2)[49]. These values are comparable to DFT bulk band masses of the STO conductionband [101, 99] for L1-L3 while they are significantly higher than the heaviest bulkmasses for H1-H2.King et al. [49] showed that this disparity between the light andheavy subbands arises due the electron-phonon interaction. For the light subbands,which have a bandwidth exceeding the Debye frequency, the dominant effect ofelectron-phonon interaction is an additional low-energy renormalization of the dis-persion clearly discernible in the form of a kink in the subband dispersion, indicatedby an arrow in Fig. 4. On the other hand, the shallow heavy bands are close to theanti-adiabatic limit and are thus subject to an overall renormalization of the entireoccupied bandwidth, which causes the increased overall effective masses.We have already discussed that these states are induced at the crystal surface andtherefore cannot be considered bulk bands. This is also evident from the observationof 5 clearly non-degenerate states at the Γ point while the conduction band mini-mum of bulk STO is formed by only three approximately degenerate bands. Theformation of multiple subbands, as well as the higher relative energy of the heavysubbands, are hallmarks of quantum confinement of the 3D bulk conduction bandnear the surface. Therefore we associate the indices 1,2 and 3 of L1-L3 and H1,H2with the principal quantum numbers of individual quantum well states. The threelight subbands all correspond to circular Fermi surface sheets while the heavy sub-bands form the long axes of cigar-shaped Fermi surface sheets, as sketched in theinset of Fig. 4(b) [86, 48]. By considering the shape of the Fermi surface sheets,the spatial anisotropy of the t g orbitals that form the conduction band of STO and Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger -0.4-0.20.0 E - E F ( e V ) -0.3 0.0 0.3 k x (Å -1 ) H2H1L3L2L1 -0.4-0.20.0 E - E F ( e V ) -0.3 0.0 0.3 k x (Å -1 ) k y k x ba Fig. 4
Electronic structure of the 2DEG at the (001) surface of SrTiO . (a) Energy momentumdispersion plot measured in the second Brillouin zone. Data shown are the sum of measurementstaken with s- and p- polarized light at 52 eV photon energy at 10 K. The arrow indicates the kink inthe disperion of the L1, L2 and L3 subbands due to electron-phonon interaction. (b) Schematic ofthe subbands resolved in the ARPES measurements of (a). The three light bands (L1, L2, L3) andthe two heavy bands (H1 and H2) are sketched in grey, green, blue, orange and coral respectively.L1, L2 and L3 have predominantly d xy -orbital character and H1,H2 have predominantly d xz / yz -orbital character. The inset shows a sketch of the corresponding Fermi surface using the samecolour scheme to distinguish between the Fermi surface sheets. Adapted from McKeown Walker et al. [62]. the polarization dependence of the photoemission matrix elements for t g states, itwas shown that the light subbands are formed by electrons in d xy orbitals, while theheavy bands have d xz / yz orbital character [86, 49, 82]. The surface 2DEG has thusthe same orbital ordering found for the LAO/STO interface 2DEG. As described inSect. 3.1.2 this is a natural consequence of quantum confinement along the [100]surface normal.Quantum well states are by definition two-dimensional and do not disperse alongthe confinement direction. Therefore, measuring the subband dispersion along k z is adirect test for the presence of quantum confinement. Experimentally this is achievedby varying the photon energy of the exciting radiation in order to probe the banddispersion perpendicular to the crystal surface. One such measurement for the STO(001) 2DEG from Ref. [103] is shown in Fig. 5. The top panel of the data-cubeshows the Fermi surface in the k x k z plane over a full Brillouin zone. The Fermiwave vectors for the first two light subbands are clearly resolved over an extendedrange of k z and are found to be constant within the accuracy of the experiment.This non-dispersive behaviour along the k z axis confirms the two-dimensional na-ture of the d xy subbands already inferred in Refs. [65, 86]. For the heavy d xz / yz sub-bands the situation is less clear. These bands have generally lower spectral weightwhich is strongly suppressed away from the bulk Γ points making it more difficultto trace their dispersion over an extended range in k z in order to unambiguously de-termine their dimensionality. Santander-Syro et al. [86] reported that the first heavysubband H1 is non-dispersive along k z and thus two-dimensional, while Plumb etal. [77] described H1 as largely three-dimensional. The dimensionality of H2 has RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 9 not been investigated in the literature to date. An independent argument for a stricttwo-dimensionality of H1 and H2 comes from their binding energies. As shownin Sect. 3.1.2 the degeneracy lifting at the Γ point between L1 and H1 as well asbetween H1 and H2 follow naturally from quantum confinement of the bulk con-duction band while alternative interpretations are not evident.The spectral weight distribution of 2D states along k z is related to the Fouriertransform of the real space wave function convolved with the k z distribution of thephotoelectron wave function. Consequently, the spectral weight distribution of 2Dstates along k z encodes information about the real space extent of their wavefunc-tions. Therefore, from the strong intensity of L1 over a full Brillouin zone in k z wecan infer that this state is mostly confined to a single unit cell along the surface nor-mal, while the limited and periodic intensity distribution of H1 indicates a more spa-tially extended wave function. This is in qualitative agreement with the tight-bindingsupercell model presented in Sect. 3.1.2, even if the complicated oscillations of thephotoemission matrix elements have so far prohibited explicit determination of thespatial extent of the wave functions of individual quantum well states. Fig. 5
Two dimensionalityof the STO (001) 2DEG. TopPanel: Constant energy mapat E F in the k x k z plane. The k z range shown is approx-imately one Brillouin zoneperpendicular to the samplesurface. The non-dispersivenature of the Fermi wavevectors along k z is indicativeof the two dimensional na-ture of the state. Front Panel:Energy-momentum subbanddispersion of the 2DEG.Adapted from Wang et al. [103]. ! ! ! ! k || ( Å -1 ) E – E F ( e V ) k z ( Å -1 )-0.2-0.40.0 3.5 5.04.54.0 0.4-0.4 0.0 The STO (001) surface 2DEG with a saturated bandwidth of ∼
250 meV de-scribed in this section has a large carrier density. Evaluating the Luttinger vol-ume of the Fermi surfaces of L1-L3 and H1 for the 2DEG shown in Fig. 4 gives n D ∼ · cm − . There is, however, a significant uncertainty in this value arisingfrom higher-order subbands with small volumes and low spectral weight that are notincluded in this estimate. Moreover, many measurements reported in the literatureresolved fewer subbands and correspondingly quote lower values for n D for thesame occupied bandwidth of L1. Despite this uncertainty, the saturated carrier den-sity of the STO (001) surface 2DEG is clearly higher than the sheet carrier densitiesreported for the LAO/STO interface 2DEG of typically n D = . − · cm − [29] and approaches the value of 0.5 electrons per unit cell ( . · cm − ) foundin the ideal polar catastrophe scenario for the LAO/STO interface. The first publications of the field [86, 65] showed that a 2DEG with virtually identi-cal band structure and density is observed on the bare fractured surfaces of La:STO,stoichiometric STO and reduced STO single crystals with bulk carrier densities up to n D ∼ · cm − . Subsequently, it was shown that the 2DEG can also be inducedon TiO terminated wafers obtained by mechanical polishing, ex situ etching anddifferent in-situ surface preparations [103, 77, 87, 17]. Fig. 6 shows the Fermi sur-face of the STO (001) 2DEG observed on TiO -terminated wafers following differ-ent in situ annealing procedures. The circular Fermi surface of the first light subbandand two cigar-like Fermi surface sheets can be seen in all cases, just as found on thefractured STO (001) surface. The characteristic features of the electronic structureand in particular the presence of multiple orbitally-ordered subbands, do not changedepending on the annealing procedure. This indicates a remarkable universality ofthe STO (001) 2DEG subband structure. It is insensitive to the bulk doping levelof the single crystal, the origin of the residual bulk doping, the marked differencesin macroscopic surface roughness between fractured and polished surfaces and thevarious terminations and reconstructions yielded by different annealing procedures. -0.50.00.5 k y ( / a ) -0.4 0.0 0.4 -0.4 0.0 0.4 -0.4 0.0 0.4 -0.4 0.0 0.4 in O in UHV in UHV Nb-STO k y ( π / a ) k x ( π /a ) b c da Fig. 6
The Fermi surface of the STO (001) 2DEG in substrates of stoichiometric STO annealedat (a) 550 ◦ C in 100 mbar O for 2 hours, (b) 300 ◦ C in UHV for 15 hours (c) 720 ◦ C in UHV for1 hour and (d) Nb:STO annealed at 550 ◦ C in 100 mbar O for 2 hours. The form of the Fermisurface is insensitive to the annealing conditions and bulk doping and is the same as observed oncleaved STO surfaces. This demonstrates the universality of the STO (001) surface 2DEG. FromPlumb et al. [77]. Santander-Syro et al. [86] first pointed out that the energetic ordering of the subbandladder in the STO (001) surface 2DEG can be understood qualitatively with a simplemodel of quantum confinement of strongly anisotropic bands with t g orbital charac-ter. As illustrated in Fig. 7(b), each t g orbital is associated with electron motion witha light effective mass along two crystallographic axes and a heavy mass along the RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 11 third direction. It follows that 2DEG subbands with a heavy in-plane effective massderive from orbitals with light out-of-plane mass m z while light subbands can haveeither a light or heavy out-of-plane mass. If bands with these orbital characteristicsare subjected to a simple wedge potential as sketched in the inset of Fig. 7(c), theyexperience an energy shift proportional to m − / z . This shift relative to the bottom ofthe potential well will be smallest for the d xy band which has light effective mass inthe surface plane and a heavy mass along the confinement direction. Thus the lowestorder d xy band will sit near the bottom of the wedge potential. Conversely the bandswith out-of-plane d xz / yz orbital character will be pushed to higher energy. This isshown in Fig. 7(c) and qualitatively reproduces experimental results from ARPESat the STO surface and from X-ray linear dichroism (XLD) of the LAO/STO inter-face [84]. It is clear however that this simple wedge model cannot accurately predictthe relative subband energies seen in ARPES experiments. their symmetry characters, discussed further below. We note that thisband structure agrees with the one depicted in Fig. 1e.We now quantitatively analyse the observed band structure. Theupperandlowerparabolicbandshavebandwidthsof210and100meVand Fermi momenta of 0.21 and 0.13 A˚ (best seen in Fig. 3), respec-tively. Thus, they correspond to light carriers with effective masses m y * < m e along k y ( m e is the free electron mass). The upper shallowband (Figs 2g, h and 3) has a bandwidth of 40meV and a Fermimomentum of k F < , corresponding to heavy carriers with m y * < m e –20 m e . The lower shallow band (Figs 2i and 3) dispersesfrom about C to about and two ellipsoids, along k x and k y , with semi-axes of0.13 and 0.3–0.4A˚ , respectively. From the area, A F , enclosed by eachFermi surface, the corresponding 2D carrier density is n A F /2 p .Accounting for the three bands that cross E F , we find 0.33 a (or about 2 cm ), where a is the cubic latticeparameter.We nowrationalize the observed electronic statesas the subbands ofa 2DEG confined within a few unit cells at the surface of SrTiO . Tothis end, we consider a potential, V , at the surface that confines the electronic motion along z (Fig. 1d, inset). This lowers the energy of thebands by about V , similar to the ‘band bending’ in semiconductorheterostructures, and produces an energy splitting between the differ-ent eigenstates that is inversely proportional to their effective massesalong z ( m z * ). The resulting subband structure, depicted in Fig. 1d,consists on a single d xy -like band and two d xz / d yz bands that are degen-erate at C . As the d xy band has a very large m z * , the attractive confiningpotential will merely pull it below E F (its energy-split eigenstates willhave a negligible separation). Thus, we identify this band with thelower parabolic band in our spectra of Fig. 2, and denote it E ( d xy ).By contrast,the d xz and d yz subbands, which are light along z , will showlarge energy splittings. They are noted E n ( d xz/yz ) ( n
1, 2,…) inFig. 1d.Other effects beyond this simplified analysis, such as spin–orbitcoupling (which has been reported at the LaAlO /SrTiO interface )and/or the low-temperature tetragonal and possibly orthorhombic dis-tortions ,canliftthedegeneracybetweenthe d xz and d yz subbands,asillustrated in Fig. 1e. This would induce a coupling, resulting in hybrid-ization between the light and heavy subbands, as indeed evidenced byour data for the lower parabolic band and the shallow bands (Fig. 3,linear vertical polarization). Another possibility would be a surfacereconstruction,althoughthisisnotsuggestedbyourdata,whichfollowsthe periodicity of the unreconstructed bulk lattice without apparent b d e d xy d yz d xz k y EE F Γ ca ΔΓ Spin–orbit + tetra + ortho + … x yz
LightHeavy E ( d xy ) E ( d xz / yz ) E ( d xz / yz ) –V k y k y EE F Γ z–V n = 1 n = 2 E F ~ eFL Ln = 10 cm –3 cm –3 cm –3 cm –3 π / a π / a n = 10 cm –2 Γ Γ Figure 1 | Electronic structure of SrTiO and effects of electronconfinement. a , Bulk conduction band of SrTiO along k y , consisting of aheavy d xz band (green) and a doublet of light d xy / d yz bands (red and blue). b , The bands in a stem from the small and large overlaps of the titanium 3 d orbitals along the y direction, depicted here for the case of 3 d xy orbitals. c , Resulting 3D Fermi surfaces (cut along the x – y plane) for several bulkdopings. The last panel shows, for comparison, the 2D Fermi surface for a2DEG of density , cm (hybridization between different Fermi surfacesheetsisnotincluded),deduced froma tight-bindingmodel .Colours indicatethe character of each Fermi surface sheet along k y . d , Quantum well states, or subbands, resulting from the confinement of electrons near the surface ofSrTiO . The inset shows a wedge-like potential created by an electric field ofstrength F at the surface, which we use as a simple model to analyse the ARPESdata (see main text). The size, L , of the confined 2DEG can be estimated fromtheextensionofthehighestoccupiedstate( n n
1) and highest occupiedstates. e , Additional degeneracy lifts at C occur as a result of spin–orbitcoupling, tetragonal and orthogonal distortions, or possible surfacereconstructions. This subband hierarchy is the one that best represents theexperimental results. RESEARCH LETTER
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Fig. 7
Modelling the effects of quantum confinement in a wedge-shaped potential well. (a) Sim-plified bulk band structure of STO along the k y axis. The colours indicate the orbital charater asindicated. (b) Cartoon of the allowed motion of an electron between d xy orbitals in a cubic struc-ture. For a band formed of such electrons, the direction in which the effective band mass wouldbe ”heavy” or ”light” is indicated. This is determined by the small or large overlap of the orbitalin that direction, respectively. (c) The subband structure expected using the approximate solutionof a particle of mass m z in a wedge potential to define the subband confinement energies at the Γ point. The inset shows the wedge potential profile as a function of z , the direction perpendicular tothe crystal surface. From Santander-Syro et al. [86]. More realistic confinement potentials can be obtained from a self-consistent so-lution of the Poisson and Schr¨odinger equations [65, 94]. Using an accurate tight-binding parametrization of the bulk conduction band and including surface bandbending as an on-site potential term in a large supercell extending several tens ofunit cells perpendicular to the surface, these calculations reproduce experimentalband structures in various quantum confined systems to a high degree of accuracy[50, 4, 48, 49, 64, 34, 110]. The subband structure for such a calculation based onan ab initio
DFT calculation of bulk cubic STO including spin-orbit coupling, is shown in Fig. 8(a). The electrostatic boundary conditions are chosen such that thetotal calculated bandwidth matches the saturated bandwidth of the 2DEG. The re-sulting confinement energies of the subbands are in good agreement with ARPESdata as demonstrated in Fig. 9(a). Such calculations can be used to estimate thefinite extent of the 2DEG along the confinement direction by projecting the eigen-states onto atomic layers as shown in Fig. 8 [49]. The confinement energy shiftsare directly related to the spatial extent of the wave functions perpendicular to thesurface, giving the intuitive result that the L1 d xy band is very spatially confined, asindicated by the high intensity of the band in Fig. 8(b). The wavefunctions of higherorder d xy bands are peaked successively further below the surface and the high in-tensity of the H1 subband in Fig. 8(d) shows that the wavefunction of the first d xz / yz band is centred 3-5 unit cells below the surface. The distribution of intensity for theheavy band shows that it is also much more spatially extended than the d xy bands.This subband-specific spatial profile of the wavefunctions reflects the form of thepotential well and is consistent with the matrix element structure seen in Fig. 5 anddiscussed in Sect. 3.1. From this it is clear that the spatial extent of the 2DEG as awhole is not a single well defined quantity. While the total charge density will al-ways peak near the surface/interface, it can have very long tails extending deep intothe bulk. These tails are often not seen in spectroscopic experiments whose signalstrengths are typically proportional to the charge density. However, they might havea strong influence on transport properties which are often dominated by the mostmobile carriers that might reside far from the interface where scattering is gener-ally lower. We also note that the shape of the confinement potential and total carrierdensity distribution in oxide 2DEGs is a strong function of carrier density. This isparticularly true for STO since the strong suppression of its dielectric constant in anelectric field progressively enhances the confinement at high carrier density. Theseconsiderations might explain why transport measurements of the LAO/STO (001)2DEG often find thicknesses >
10 nm [6, 79], while spectroscopic studies and DFTcalculations typically report a confinement of the 2DEG within < ab-initio electronic structure calculations of STO surface 2DEGs have beenpresented in Refs. [2, 33] and qualitatively agree with the results of tight-binding su-percell calculations. While such calculations are suitable for studying the behaviourof oxygen vacancies, direct comparison of the resulting band structure with exper-iment is hindered by limitations in the size of the supercell and the ordered natureof vacancy arrangements in density functional calculations that impose translationalinvariance in the surface plane. The confinement potential associated with a surface 2DEG inherently breaks inver-sion symmetry, which lifts the constraint of spin degeneracy from the band struc-ture. Spin splitting may result due to the coupling of an electron’s motion to itsspin via the effective in-plane magnetic field resulting from a Lorentz transforma-
RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 13 -0.25-0.20-0.15-0.10-0.050.00 E - E F ( e V ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) maxmin -0.6 -0.4 -0.2 0.0k || (Å -1 ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) -0.6 -0.4 -0.2 0.0k || (Å -1 ) st u.c. 2 nd u.c. 3 - 5 u.c. 6 - 10 u.c. 11 - 18 u.c. 19 - 30 u.c. a b c d e f g Supplementary Figure 3.
Spatial extent of the 2DEG.
Layer-projected calculations of theelectronic structure of the SrTiO Fig. 8
Layer-projected tight binding superecell calculations of the electronic structure of the STO(001) surface 2DEG integrated over (a) the full 30 unit cell supercell, and (b)-(e) individual or fewunit cell regions as labelled in the figure. High intensity (yellow) corresponds to a high wavefuncionweight. This calculation is based on and ab initio
DFT parametrization of bulk STO, including afield dependent dielectric constant as proposed in references [94, 19] and implements electronstaticboundary conditions that reproduce the overall bandwidth of the 2DEG. From King et al. [49]. tion of the symmetry-breaking electric field at the surface. This is known as theRashba spin-orbit interaction [10]. The magnitude of spin-splitting in a Rashba sys-tem is linearly proportional to the strength of the electric field. This behaviour isobserved in conventional semiconductor 2DEGs [74] and is a prerequisite for manyapplications in spintronics such as the spin-field effect transistors (spin-FET) [55].Rashba spin-splitting is also expected to scale with the strength of the atomic spin-orbit interaction (SOI) in the host material. Therefore considering the light atomicmasses of the constituent elements of STO and consequently small atomic SOI, asmall Rashba effect might na¨ıvely be expected in STO based 2DEGs. Surprisinglythough, a substantial gate-tunable spin splitting of 2 −
10 meV has been deducedfrom transport experiments for both the LAO/STO interface 2DEG [13, 38, 31, 57]and electrolyte-gated STO [73]. The spin-splitting was found to have a stronglynon-linear dependence on gate-field and weak antilocalization measurements sug-gest that it is proportional to k rather than being k -linear as expected in the simplestmodels of Rashba spin splitting [73].Using band structure calculations based on relativistic DFT shown in Fig. 9(c)and (d), Zhong et al. [112] demonstrated that these behaviours can be understoodas the signatures of an unconventional Rashba spin-splitting arising from the multi-orbital nature of 2DEGs in STO. Fig. 9(d) shows the band structure for a singleLAO/STO interface. In the region of the avoided crossings of light and heavy sub-bands the spin splitting is dramatically enhanced and clearly deviates from a k -linearform. A strikingly similar spin structure of the STO surface 2DEG can be seenin the tight binding supercell (TBSC) calculations of references [49] and [64] asshown in Fig. 9(a) and (b) and has been found by several other theoretical studies[43, 49, 45, 46, 91, 100, 113]. The authors of reference [49] related this enhance-ment to the finite orbital angular momentum that arises at the crossings of bands ofdifferent orbital character and augments the spin-orbit interaction at these particularlocations in momentum-space. In this case the gate voltage used in transport exper-iments not only directly tunes the Rashba coefficient in STO 2DEGs, but indirectly a bdc -0.3-0.2-0.10.0 -0.5 0 0.5 E - E F ( e V ) k x (!/a) k x (!/a) -0.050 0.40.30.2 E n e r g y ( e V ) k x (!/a) x (π / a)1.881.901.92 Fig. 9
Unconventionl Rashba-like spin splitting of STO (001) 2DEG subband structures. (a) DFTband structure of a single n -type vacuum/LAO/STO interface. (b) The boxed region in (a) is en-larged which reveals that the bands are not spin degenerate, and that spin-splitting is enhanced at theavoided crossings of light and heavy subbands. (c) Band structure of the STO surface found fromtight-binding supercell calculations based on ab initio DFT electronic structure of bulk STO (blacklines), overlayed on ARPES data (grascale image) of the STO (001) surface2DEG. This showsgood agreement with the experimental confinemnt energies and many similarities with the inter-face calculation in (a). (d) The boxed region in (c) is enlarged and shows a similar spin-splittingas seen in (b) for the LAO/STO interface. In (a),(b) and (d) opposite in-plane spin channels arecoloured red and blue. Adapted from Zhong et al. [112] and McKeown Walker et al. [64]. tunes the spin splitting by controlling the band filling and band structure. Indeedthis indirect electrostatic tuning may be more important in such a system since thespin splitting is enhanced by approximately an order of magnitude at the avoidedcrossings of the d xz / yz and d xy bands. However, this unconventional spin-splittingnever exceeds ∼
10 meV and thus remains below the resolution of high-resolutionARPES measurements such those of Fig. 4.In order to gain direct spectroscopic insight into the spin structure of the STO(001) surface 2DEG Santander-Syro et al. [87] and McKeown Walker et al. [64]performed spin and angle resolved photoemission spectroscopy (SARPES) exper-iments. However, these authors reported conflicting results. McKeown Walker etal. measured no significant spin polarization of the photocurrent above the ∼ RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 15 noise level of their experiment. Considering the complex subband structure andpoor experimental resolution in SARPES, they reason that such a negligible pho-tocurrent polarization is fully consistent with the spin splitting shown in Fig. 9.However, direct experimental confirmation of this unconventional Rashba effect re-mains elusive. Conversely Santander-Syro et al. measured a large polarization ofthe photocurrent which prompted them to propose an entirely new interpretationof the universal subband structure measured at the surface of STO (001) crystals.They propose that bands L1 and L2 are the fully spin polarized components of asingle d xy subband. In a Rashba system the spin states must be degenerate at theBrillouin zone centre. However, it is well established that L1 and L2 of the STOsurface 2DEG are not degenerate. Santander-Syro et al. speculate that the presenceof ferromagnetic domains, which generate a large Zeeman-like term lifting the Γ point degeneracy, could account for this. Indeed some DFT calculations for orderedoxygen vacancy arrangements at the STO (001) surface show magnetic solutions ofcomparable energy to the paramagnetic case [2, 33]. However, in these calculationsthe remnant in-plane spin component due to the Rashba effect is an order of magni-tude smaller than that measured by Santander-Syro et al. . To date, the origin of thediscrepancy between these two SARPES experiments is unclear and the details ofthe spin structure remain elusive. (111) and (110) surface 2DEGs Two-dimensional electron gases in ABO transition metal oxides oxides are by nomeans restricted to the (001) plane. 2DEGs have been successfully engineered atthe bare (111) and (110) surfaces of SrTiO [104, 63, 80] and at interfaces withthese orientations [37, 3, 78]. These studies are motivated, in part, by theoreticalpredictions of novel ferromagnetic and ferroelectric states and topological phases in(111) bilayers of cubic perovskites [108, 24] and the intrinsic in-plane anisotropy ofthe (110) plane. In the following we will discuss the overall electronic structure of(111) and (110) orientated surface 2DEGs on STO and relate it to the framework forquantum confinement developed in Sect. 3.1.2 and its interplay with the differentsymmetries of these surfaces.Fig. 10 (a) shows the Fermi surface of the STO (111) surface. Three intersect-ing elliptical Fermi surface sheets with an overall six-fold symmetry can be seen.Each of these can be associated with the projection of a single t g component ofthe conduction band onto the (111) plane. As seen in Fig. 10 (b), which shows thebands dispersing along the long axis of one ellipse, within the accuracy of the ex-periment these electron like bands are degenerate at the Γ point. This is a naturalconsequence of the 120 ◦ rotational equivalence of the t g orbitals in the (111) plane,which causes all three bands to have the same effective mass along the confinementdirection. When applied to the STO (110) plane, these arguments predict degeneratebands of d xz / yz character, due to the ”semi-heavy” hopping for these orbitals, and a d xy band with weaker confinement. This is indeed the case, as seen in Fig. 11(a) Fig. 10
Electronic structure of the STO (111) surface 2DEG. (a) Fermi surface showing threeelliptical Fermi surface sheets. The black hexagon indicates the surface Brilluion zone and theBlack dot indicates the Γ point. (b) Dispersion along the Γ -M (cid:48) direction. Spectral weight at theFermi level is from a second subband. (c) Projection onto the (111) plane (red shape) and cut at the Γ point (black lines) of a model STO bulk Fermi surface. The form of the STO (111) 2DEG Fermisurface closely ressembles the projection. Adapted from McKeown Walker et al. [63]. and (b) which shows the Fermi surface and a band dispersion from the STO (110)2DEG [104]. Thus the STO (110) 2DEG is orbitally polarized, although the rela-tively small variation between the band masses for the d xz / yz and d xy bands alongthe [110] direction leads to a much less dramatic orbital reconstruction than foundfor the STO (001) 2DEG. and less dependent on the chemical complexity inherent to in-terfacial 2DEGs. The (110) 2DEG turns out to be strikinglydifferent from the (001) 2DEG, which has been the subject ofprevious ARPES studies. The band dispersion is not only distinctfrom the one of the bulk, it even depends on the quantum number for the (110) confinement. Hence one can engineera completely flat band along ½ " , offering good prospects tofind exotic properties in the future. For example, as was shownfirstly in ref. 23, a flat band naturally leads to so-called “ flat-bandferromagnetism, ” hence offering a route to spin-polarized currents. k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) D H C
A B G F E
LV LV LH LH
Fig. 3.
ARPES of the electronic structure at SrTiO (110)-(4 × A – D ) Energy-momentum intensity maps ( T sample = K, h ν = eV) along the Γ − M (or [001])direction and the Γ − M (or ½ " ) direction, respectively. ( E – H ) Corresponding second derivatives. In each direction, the spectra were measured with linearvertical ( A and D ) and linear horizontal ( B and C ) polarized light. Tight-binding fits are overlaid for both directions. The d xy -like bands are drawn in blue andthe d yz = d zx -like bands in red. The d xy -derived bands are weakly dispersive and d yz = d zx -derived bands are strongly dispersive along [001]; the d yz = d zx -derivedbands become weakly dispersive and d xy -derived band becomes strongly dispersive along ½ " . The subbands become more visible in E – H . E B =0 meV E B =30 meV E B =60 meVM Z Г DCBA d xy d yz / d zx k M (Å -1 ) k M (Å -1 ) k Z (Å -1 ) k Z ( Å - ) k Z ( Å - ) k M (Å -1 ) k M (Å -1 ) Fig. 4.
Overview of the electronic structure. ( A ) Full photoemission mapping and ( B – D ) constant energy cuts at different binding energies (E B =
0, 30, and 60 meV)and schematic constant-energy surfaces (
Lower ). Data taken with LV light, which emphasizes d yz and d zx orbitals. These appear bright, whereas d xy -derived statesappear faint. In the schematics the reconstructed (4 ×
1) Brillouin zone is indicated by dotted lines. Note that the Fermi surface lies in the (1 ×
1) Brillouin zone,consistent with the 2DEG being confined at the SrTiO layers beneath the surface reconstruction. At higher binding energy, E B =
60 meV, only the d yz = d zx -derivedellipsoid is occupied. The resulting constant-energy surface is strongly anisotropic compared with the bulk projected energy surface (black dashed ellipsoid). | and less dependent on the chemical complexity inherent to in-terfacial 2DEGs. The (110) 2DEG turns out to be strikinglydifferent from the (001) 2DEG, which has been the subject ofprevious ARPES studies. The band dispersion is not only distinctfrom the one of the bulk, it even depends on the quantum number for the (110) confinement. Hence one can engineera completely flat band along ½ " , offering good prospects tofind exotic properties in the future. For example, as was shownfirstly in ref. 23, a flat band naturally leads to so-called “ flat-bandferromagnetism, ” hence offering a route to spin-polarized currents. k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) D H C
A B G F E
LV LV LH LH
Fig. 3.
ARPES of the electronic structure at SrTiO (110)-(4 × A – D ) Energy-momentum intensity maps ( T sample = K, h ν = eV) along the Γ − M (or [001])direction and the Γ − M (or ½ " ) direction, respectively. ( E – H ) Corresponding second derivatives. In each direction, the spectra were measured with linearvertical ( A and D ) and linear horizontal ( B and C ) polarized light. Tight-binding fits are overlaid for both directions. The d xy -like bands are drawn in blue andthe d yz = d zx -like bands in red. The d xy -derived bands are weakly dispersive and d yz = d zx -derived bands are strongly dispersive along [001]; the d yz = d zx -derivedbands become weakly dispersive and d xy -derived band becomes strongly dispersive along ½ " . The subbands become more visible in E – H . E B =0 meV E B =30 meV E B =60 meVM Z Г DCBA d xy d yz / d zx k M (Å -1 ) k M (Å -1 ) k Z (Å -1 ) k Z ( Å - ) k Z ( Å - ) k M (Å -1 ) k M (Å -1 ) Fig. 4.
Overview of the electronic structure. ( A ) Full photoemission mapping and ( B – D ) constant energy cuts at different binding energies (E B =
0, 30, and 60 meV)and schematic constant-energy surfaces (
Lower ). Data taken with LV light, which emphasizes d yz and d zx orbitals. These appear bright, whereas d xy -derived statesappear faint. In the schematics the reconstructed (4 ×
1) Brillouin zone is indicated by dotted lines. Note that the Fermi surface lies in the (1 ×
1) Brillouin zone,consistent with the 2DEG being confined at the SrTiO layers beneath the surface reconstruction. At higher binding energy, E B =
60 meV, only the d yz = d zx -derivedellipsoid is occupied. The resulting constant-energy surface is strongly anisotropic compared with the bulk projected energy surface (black dashed ellipsoid). | and less dependent on the chemical complexity inherent to in-terfacial 2DEGs. The (110) 2DEG turns out to be strikinglydifferent from the (001) 2DEG, which has been the subject ofprevious ARPES studies. The band dispersion is not only distinctfrom the one of the bulk, it even depends on the quantum number for the (110) confinement. Hence one can engineera completely flat band along ½ " , offering good prospects tofind exotic properties in the future. For example, as was shownfirstly in ref. 23, a flat band naturally leads to so-called “ flat-bandferromagnetism, ” hence offering a route to spin-polarized currents. k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k Z (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) k M (Å -1 ) . . . E B ( e V ) D H C
A B G F E
LV LV LH LH
Fig. 3.
ARPES of the electronic structure at SrTiO (110)-(4 × A – D ) Energy-momentum intensity maps ( T sample = K, h ν = eV) along the Γ − M (or [001])direction and the Γ − M (or ½ " ) direction, respectively. ( E – H ) Corresponding second derivatives. In each direction, the spectra were measured with linearvertical ( A and D ) and linear horizontal ( B and C ) polarized light. Tight-binding fits are overlaid for both directions. The d xy -like bands are drawn in blue andthe d yz = d zx -like bands in red. The d xy -derived bands are weakly dispersive and d yz = d zx -derived bands are strongly dispersive along [001]; the d yz = d zx -derivedbands become weakly dispersive and d xy -derived band becomes strongly dispersive along ½ " . The subbands become more visible in E – H . E B =0 meV E B =30 meV E B =60 meVM Z Г DCBA d xy d yz / d zx k M (Å -1 ) k M (Å -1 ) k Z (Å -1 ) k Z ( Å - ) k Z ( Å - ) k M (Å -1 ) k M (Å -1 ) Fig. 4.
Overview of the electronic structure. ( A ) Full photoemission mapping and ( B – D ) constant energy cuts at different binding energies (E B =
0, 30, and 60 meV)and schematic constant-energy surfaces (
Lower ). Data taken with LV light, which emphasizes d yz and d zx orbitals. These appear bright, whereas d xy -derived statesappear faint. In the schematics the reconstructed (4 ×
1) Brillouin zone is indicated by dotted lines. Note that the Fermi surface lies in the (1 ×
1) Brillouin zone,consistent with the 2DEG being confined at the SrTiO layers beneath the surface reconstruction. At higher binding energy, E B =
60 meV, only the d yz = d zx -derivedellipsoid is occupied. The resulting constant-energy surface is strongly anisotropic compared with the bulk projected energy surface (black dashed ellipsoid). | ba Fig. 11
Electroninc structure of the STO (110) surface 2DEG. (a) Fermi surface showing twointersecting elliptical Fermi surface sheets. The d xz / yz band are degenerate and have higher intensityhere due to the polarization of the exciting radiation. (b) Disperion along the k ¯ Z direction. Thedashed red(blue) lines indicate the dispersion of the d xz / yz ( d xy ) states and possible higher ordersubbands. Adapted from Wang et al. [104]. Notably the two dimensional carrier densities of the fully saturated 2DEGs onall three low index surfaces of STO are comparable to each other, with n D ∼ · cm − . Additionally, models reproducing the saturated band structures ofboth the (111) and (001) 2DEGs find very similar confinement fields at the surface RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 17 [63, 49]. This suggests a common origin for the saturation of the 2DEG bandwidthcontrolled by a physical limit on the electric field strength at the surface. One pos-sible mechanism for such a limit could be the onset of diffusion of charged oxygenvacancies as the electric field increases. The common carrier density implies that2DEGs on different low index surfaces will have different bandwidths and spatialextents. This is evident from the dispersion plots of Figs. 11,10 and 4 and photonenergy dependent measurements that demonstrate the extended nature of the elec-tron density of (110) and (111) 2DEGs, in analogy to the heavy d xz / yz band of theSTO (001) 2DEG.Both the STO (111) and (110) surfaces show dramatic in plane subband massenhancements with respect to the dispersion of bulk carriers along the same direc-tion. As shown in Refs. [63, 104] this is an intriguing effect of quantum confine-ment, rather than a manifestation of many-body interactions. Intuitively this massenhancement can be understood as the result of the projection of the three dimen-sional bulk Fermi surface onto a 2D plane. As illustrated in Fig. 10 for the (111)plane, the contours of the projection (red) are elongated with respect to those ofthe bulk dispersion in that plane (black lines) and thus correspond to higher effec-tive masses. An alternative way of thinking is that the in-plane subband mass isenhanced as a result of the zig-zag hopping of carriers moving in the surface plane,which, in conjunction with surface band banding leads to reduced hopping elementsand thus enhanced effective masses in-plane.Along both the [111] and [110] directions SrTiO can be viewed as a stack ofcharged planes. Therefore the charge accumulation mechanism at (111) or (110)surfaces might be expected to be different from what is observed for the neutrallystacked [001] direction. For example, surface reconstructions that compensate thepolarity of the surface could induce spontaneous charge accumulation. However theorigin of the (111) and (110) surface 2DEGs has very much the same phenomenol-ogy as the (001) surface, as discussed in Sect. 2.1. Additionally, there is no evi-dence from ARPES that surface reconstructions influence the (111) and (110) sur-face 2DEG band structures. For the case of the STO (110) 2DEG where the surfaceis known to have a 4 × etal. proposed that light-induced oxygen vacancies migrate below the overlayer anddope electrons which are not perturbed by the potential of the surface reconstruc-tion. For the case of the STO (111) 2DEG, where details of the surface terminationare not known, the insensitivity of the states to possible reconstructions was at-tributed to the wavefunctions of the 2DEG being centred far below the surface. Theenvelope wavefunction solutions of the self-consistent tight binding supercell cal-culations [63] show the wavefunctions peak ≈ (001) surfaces, where the d xy subbands are more tightly confined at the surface [105]. It may also providethese systems with some degree of insensitivity to surface or interface impurities. The diverse bulk properties of the large number of transition metal oxides suitablefor heteroepitaxy hold much potential for both fundamental studies and applica-tions. Inducing 2DEGs in insulating oxides other than STO is an important steptowards unlocking this potential. However, so far little is known about the prerequi-sites on host materials and interface properties required to this end. To date, besideson SrTiO , highly itinerant surface 2DEGs have been observed on KTaO [48, 85, 5]and anatase TiO [81, 105] which both have an empty d -shell in stoichiometric form,while attempts to induce a 2DEG in rutile TiO and the Mott insulator LaTiO wereunsuccessful [81, 61]. In the case of rutile TiO , this might be related to the strongtendency of bulk samples to localize excess carriers. Hole doped bulk LaTiO onthe other hand, is known to host itinerant carriers [96] suggesting that its fundamen-tal material properties should not prohibit the formation of 2DEGs. This highlightsone of the key challenges of this field. While it is clear that the creation of a 2DEGrequires chemical doping or charge transfer across an interface, it is often hard topredict whether carrier doping of insulating oxides induces metallicity. KTaO shares important properties with SrTiO . Both are ABO perovskites withempty d -shell and are close to a ferroelectric instability. However, unlike in STO, thebulk truncated (001) surface of KTO is strongly polar. Additionally, in KTO the ef-fective masses of the conduction band are lighter and the spin-orbit interation in theTa 5 d shell is more than an order of magnitude larger than in the Ti 3 d states. Thissuggests that KTO might be a suitable material on which to engineer 2DEGs withhigh mobility and large tunable Rashba splitting. However, the lack of establishedsurface preparation recipes resulting in well-ordered surfaces with single termina-tion and the poor stability of the KTO (001) surface at high temperature have thusfar prohibited the growth of heteroepitaxial interfaces with a quality as it is rou-tinely achieved with STO substrates. Indeed, KTO based 2DEGs were first inducedwith a parylene gate dielectric [72] and by electrolyte gating [97], while the first ox-ide interface inducing a 2DEG in KTO was only reported recently [115]. Notably,these studies found superconductivity at high carrier density [97] and reported spin-precession lengths that are significantly shorter than in InGaAs and tunable over avery wide range varying from 20 to 60 nm with gate voltage [72] suggesting muchpotential of KTO for spintronic devices. Yet, the Rashba effect which causes thespin-precession and even the overall band structure of KTO based 2DEGs remainpoorly understood.King et al. reported a 2DEG on the bare (001) surface of KTO and studied itsband structure with a combination of ARPES and tight-binding supercell calcula-tions [48]. The experimental data showed an occupied band width of ∼
400 meVand resolved two isotropic light subbands with effective masses of ∼ . e and RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 19 a shallower subband with m ∗ ∼ − e contributing an elliptical Fermi surface.These results were confirmed by Santander-Syro et al. [85] and could largely bereproduced by band structure calculations although the agreement is not as goodas in STO (001). In particular, finer details, such as hybridization gaps between thesubbands and the theoretically predicted Rashba splitting could not be resolved ex-perimentally. From the line width, King et al. deduced a upper limit for the Rashbasplitting of ∼ .
02 ˚A − [48], which is consistent with the spin precession lengthsreported in Ref. [72] but still more than an order of magnitude lower than in othersurface systems containing heavy atoms, such as the L-gap surface state on Au(111)[56] or the surface 2DEG on the topological insulator Bi Se [47].The authors of Ref. [48] attributed the modest Rashba splitting in KTO to theparticular orbital character of the bulk states from which the 2DEG derives. Thestrong spin-orbit interaction in KTO restores the orbital angular momentum, whichis largely quenched in the 3 d counterpart STO. Its conduction band is thus moreappropriately described by total angular momentum states rather than the crystalfield eigenstates commonly used in STO. The conduction band edge at the Γ pointof KTO is formed by a quartet of J eff = / t g orbitals. The J eff = / ∆ SO ≈
400 meV. This splitting is larger than the occupied band width of KTO based2DEGs reported in the literature [48, 85], which therefore derive from the J eff = / TiO crystallizes in the rutile and anatase structures and is one of the most intenselystudied TMOs due to its diverse applications in heterogeneous catalysis, photo-catalysis, gas-sensing or photovoltaics and its use as transparent conductive coat-ing or simply as biocompatible white pigment. While the surface science of TiO is intensely studied [23], TiO has so far received less attention as a host materialfor oxide 2DEGs and only a few studies reported conductive interfaces with otherTMOs [68, 88]. Similar to STO, TiO is susceptible to the creation of light-inducedoxygen vacancies [54, 71], which was exploited by Moser et al. [71] to dope anatasebulk single crystals and PLD-grown thin films inducing quasi-3D electronic stateswhich showed strong signatures of electron-phonon interaction in the ARPES spec-tra. Subsequently, R¨odel et al. showed that under appropriate conditions fully 2Dquantum confined states with the characteristic subband ladder of a 2DEG can beinduced on the (001) and (101) surface of anatase TiO [81]. Intriguingly though,the same approach did not induce itinerant carriers in rutile TiO [81]. Unlike in STO, the conduction band minimum of anatase TiO is of pure d xy orbital character with the other t g orbitals split off by ∼ . based 2DEGs with isotropicFermi surfaces of all subbands on the (001) surface and concentric elliptical Fermisurfaces on the (101) surface [81]. The d xy orbital character of anatase TiO based2DEGs also leads to a particularly strong confinement of the carriers in a narrowlayer below the surface. This was exploited by Wang et al. to demonstrate a peri-odic lateral modulation of the 2DEG by the ( × ) surface reconstruction of in-situ grown anatase TiO thin films with (001) orientation [105]. Tuning the Fermi wavevector of the first subband to coincide with the superlattice Brillouin zone bound-ary corresponding to the surface reconstruction, the authors of Ref. [105] found asizeable superlattice band gap at the Fermi level, as shown in Fig. 12. This suggestsa new route towards electronic structure engineering in oxide 2DEGs by exploitingthe ubiquitous surface reconstructions of TMOs. -0.2-0.10.00.1 E - E F ( e V ) k x ( π /a) -0.3-0.10.0 E - E F ( e V ) k x ( π /a) -0.050.00 2.42.32.2 a b Fig. 12 (a) 2DEG subband dispersion at the surface of anatase TiO (001) thin film terminated by a ( × ) surface reconstruction. Backfolding of the n = ×
30 supercell with anin-plane potential modulation of ∼
100 meV estimated from ab-initio calculations of core-levelsimposed in the topmost unit cell. For details see Wang et al. [105].
The thermodynamic and transport properties of transition metal oxides are oftendominated by many-body interactions. Prominent examples include high tempera-ture superconductivity in cuprates, colossal magnetoresistance in manganites or theubiquitous metal-insulator transitions in ultrathin TMO films [109, 52]. Unlockingthe full potential of TMO 2DEGs will require an improved understanding of theseinteractions as the interfacial carrier density is tuned, which is a formidable task.Here, we briefly review the first microscopic measurements of many-body interac-tions in oxide surface 2DEGs using ARPES [71, 49, 17, 103]. These studies all focuson electron-phonon interaction (EPI) in anatase TiO and SrTiO as the density of RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 21 itinerant carriers is tuned by controlling the oxygen vacancy concentration using themethods described in Sect. 2.1.Electron-phonon interaction in STO dominates the mobility of interface 2DEGsat elevated temperatures [67], contributes to the large thermoelectric coefficient ofdepleted 2DEGs [75] and has been invoked as the pairing glue for superconductiv-ity [27, 35]. Yet, until recently little was known about its nature and strength. Due toits strongly ionic character, lightly doped STO was often considered a model systemfor the nonlocal Fr¨ohlich interaction describing the dielectric screening of an excesscharge by longitudinal optical (LO) phonons [21]. In this model, EPI is stronglypeaked at small momentum transfer Q and dominated by coupling to the highestLO branch [21]. On the other hand, STO is well known for its large static dielec-tric constant implying soft transverse modes, which can eventually condense into aferroelectric state [39, 83]. A recent theoretical study found that coupling to sucha soft mode near a quantum critical point reproduces the supercondcuting dome ofSTO [27].Early experimental studies of EPI in STO focused on doped bulk samples. VanMechelen et al. [101] and Devreese et al. [22] showed that a pronounced mid-infrared peak in optical spectra can be reproduced quantitatively by the Fr¨ohlichmodel with a moderate coupling constant of α ≈ m ∗ / m band ∼ − et al. [16] reported signatures consistent with coupling to the highestLO phonon branch with frequency Ω LO , ≈
100 meV, as observed by van Meche-len et al. [101], while Meevasana et al. [66] reported a perturbative EPI with muchstronger coupling to a soft LO mode than expected in the Fr¨ohlich model. Whilethis discrepancy was never fully resolved, we speculate that it arises at least partiallyfrom accidental surface doping in the latter study. The ARPES study by Moser etal. of quasi-3D carriers in anatase TiO created by photo-induced oxygen vacanciesreported replica bands characteristic of Fr¨ohlich polarons at low carrier density anda progressive screening of EPI with increasing density [71] which has similaritiesto what is observed in STO (001) as will be described in detail in this section.The marked influence of the carrier concentration on the spectral function is evi-dent from the data on the STO (001) surface 2DEG of Wang et al. [103] reproducedin Fig. 13. Using in-situ prepared surfaces, these authors could reduce the vacancyformation rate permitting a systematic study of the spectral function for carrierdensities spanning nearly an order of magnitude from ∼ · − · cm − .At the lowest densities corresponding to an occupied quasiparticle bandwidth of ∼
20 meV, the spectra of Ref. [103] show dispersive replica bands shifted by mul-tiples of 100 meV to higher energy. This implies preferential coupling with smallmomentum transfer ( Q (cid:28) π / a ) to the LO mode of STO, which is the hallmark ofFr¨ohlich polarons, quasiparticles formed by an excess electron dressed by a polar-ization cloud extending over several lattice sites that follows the charge as it prop-agates through the crystal [21, 71, 17]. Fig. 13(g) shows that the spectral weight -0.3 0.0 0.3 k x (Å -1 ) -0.3 0.0 0.3 k x (Å -1 ) -0.4-0.20.00.2 E - E F ( e V ) -0.3 0.0 0.3 k x (Å -1 ) -0.3 0.0 0.3 k x (Å -1 ) I n t en s i t y ( a r b . un i t s ) -0.4 -0.2 0.0 E - E F (eV) -0.4 -0.2 0.0 E - E F (eV) -0.4 -0.2 0.0 E - E F (eV) -0.4 -0.2 0.0 E - E F (eV)-0.3 0.0 0.3 k x (Å -1 ) -0.3 0.0 0.3 k x (Å -1 ) -0.4 -0.2 0.0 E - E F (eV) Σ ( m e V ) -0.2 -0.1 0.0 E - E F (eV) Σ '' Σ ' -0.4 -0.2 0.0 E - E F (eV) Fig. 13
Evolution of the spectral function in the STO (001) surface 2DEG with increasing carrierdensity. (a-f) Raw dispersion plots and MDCs extracted at the Fermi level. Carrier densities areindicated in units of cm − . (g-l) EDCs at the Fermi wave vector k F indicated in the image plots.Fits in (g-j) use a Franck-Condon model with a single phonon mode of 100 meV. The thin blueline in (l) is a spectral function calculated for the conventional Eliashberg self-energy in the high-density limit reported in Ref. [49] and shown in the inset. Adapted from Wang et al. [103]. at this density is clearly dominated by excitations involving one or more phonons(blue peaks in Fig. 13). The quasiparticle residue, which gives the relative spectralweight of the coherent quasiparticle (yellow in Fig. 13), was observed to be Z ≈ . α ≈ . α .Concomitant, the mass enhancement m ∗ / m band decreases from 2.4 m e to 1.7 m e , fol-lowing the trend m ∗ / m band = / ( − α / ) expected for Fr¨ohlich polarons at interme-diate coupling strengths [21]. Using exact diagonalization, the authors of Ref. [103]showed that the observed evolution of EPI can be traced back to a gradual transi-tion from dielectric screening at low density to dominantly electronic screening athigh density qualitatively consistent with earlier ARPES measurements on quasi-3Dstates in oxygen deficient anatase TiO [71]. Superconducting susceptibilities cal-culated within the same approach further showed that the dominant pairing channelhas s -wave symmetry and indicated that a competition between the opposite trendsof density of states and effective coupling strength underlies the dome shaped su-perconductivity observed at the LAO/STO interface [14].It is worth noting that the effect of increasing carrier density in the STO (001)2DEG is not limited to progressive screening of the long-range Fr¨ohlich interaction.At the saturation density of the surface 2DEG, the LO mode is almost completely RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 23 screened as is evident from the absence of any spectral signatures at 100 meV inFig. 13(f). However, the coupling to lower frequency modes increases far beyond thepredictions of the Fr¨ohlich model [102, 66, 49] pointing at a remarkable complexityof EPI in oxide 2DEGs. We also point out that a significant coupling to the softferroelectric mode predicted in Ref. [27] cannot be excluded from published ARPESdata on surface or interface 2DEGs in STO due to the difficulty of quantifying thequasiparticle dispersion at very low energy.Electron-phonon interaction at the LAO/STO interface has recently been studiedby tunneling spectroscopy and soft X-ray ARPES. Investigating tunnel junctions tointerface 2DEGs with ∼
30 meV occupied bandwidth, Boschker et al. [8] foundinelastic tunneling attributed to EPI with dominant coupling to the LO mode andprogressively weaker contributions from the softer LO modes of STO. Varying thechemical potential over ∼ mode is in agreement with the ARPES results on the STO (001) surface 2DEGfor similar bandwidths [103]. The results on the surface 2DEG of Ref. [104] werefurther confirmed by a soft X-ray ARPES study of an LAO/STO interface with n D ≈ · cm − [11], reporting a replica band and Z ≈ . The study of 2DEGs at the surface of 3D transition metal oxides is clearly moti-vated by the importance of interface 2DEGs for oxide electronics. However, sincethe first discovery of surface 2DEGs on STO (001) in 2011 [65, 86], their investiga-tion by ARPES has, to some extent, evolved into its own sub-field with a number ofinteresting results from several groups as summarized in this chapter. These includethe comprehensive characterization of the subband masses, the subband orderingand the resulting orbital polarization for different surface planes and the rational-ization of these effects in terms of quantum confinement [65, 86, 48, 49, 63, 104];the identification of light-induced oxygen vacancies as the microscopic origin ofthe 2DEG carriers which has permitted tuning of the carrier density over a widerange [65, 63, 62]; and the observation of a complex evolution of electron-phononinteraction with carrier density giving rare microscopic insight into the many-bodyinteractions governing important properties of oxide 2DEGs [49, 103, 17]. Mostof these studies have focused on different surface orientations of STO but 2DEGshave also been induced and studied at low-index surfaces of KTaO and anataseTiO [48, 85, 81, 105]. While these results are interesting in their own right, their relation with the prop-erties of interface 2DEGs is not always clear. This being said, for the intensely stud-ied STO (001) 2DEG a number of experiments suggest that some important proper-ties are universal in the sense that they are largely determined by the host materialand crystallographic orientation, rather than by structural details or the origin of thecharges. For instance, orbital polarization is evident in the surface 2DEG [86, 48, 49]and has also been measured directly for the LAO/STO interface using X-ray lin-ear dichroism [84]. The Rashba spin-splitting of the surface 2DEG discussed inRefs. [49, 64] is also in fair agreement with weak antilocalization and quantum os-cillation measurements and calculations of interface 2DEGs [13, 30, 38, 57]. More-over, the nature and strength of electron-phonon interaction at both the bare STO(001) surface and the LAO/STO (001) interface were found to be in good agree-ment [103, 8, 11]. The universality of electronic properties is further supported by arecent experiment demonstrating that room temperature deposition of ≈ terminated STO (001) wafer surface donates electrons and induces a 2DEG inSTO [82] by strongly reducing the surface. As seen in Fig. 14 the subband structureof this 2DEG bears all the hall marks of the STO surface 2DEG, while in fact itexists at the interface of STO and aluminium oxide. -1.8-1.6-1.4 k y ( Å - ) -0.2 0.0 0.2k x ( Å -1 ) -0.2-0.10.0 E - E F ( e V ) x ( Å -1 )-0.2-0.10.0 E - E F ( e V ) x ( Å -1 ) a b c Fig. 14
Electronic structure of the 2DEG at the interface of STO (001) and aluminium oxideformed when 2 ˚A Al is deposited on the bare TiO terminated (001) surface of STO at room tem-perature. A redox reaction at the interface occurs and the surface of STO becomes reduced anddoped with itinerant electrons which have the Fermi surface shown in (a). The Luttinger volumeof these two concentric circular Fermi surface sheets is as found for the 2DEG at the bare (001)surface. The electron dispersions along the k x axis are shown in (b) and (c) for orthogonal polar-izations of the exciting radiation revealing the light d xy and heavy d xz / yz bands respectively. Thisorbital polarization is the same as found for the 2DEG at the bare (001) surface. Adapted fromR¨odel et al. [82]. On the other hand, some basic 2DEG properties such as the carrier density andoccupied bandwidth remain controversial. For the surface 2DEGs discussed in thischapter, the latter is evident from the ARPES data while the total carrier concentra-tion and density of states at the Fermi level are difficult to determine experimentallysince the closely spaced shallow subbands predicted by band structure calculationshave so far eluded detection. In interface systems, both carrier density and band-width are difficult to quantify. The Hall effect, commonly used as a measure of the
RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 25 carrier density, is strongly non-linear for the LAO/STO interface and its quantitativerelation to the itinerant carrier density is model dependent [28]. Furthermore esti-mates of the occupied bandwidth based on quantum oscillation and spectroscopicmeasurements range from ≈ ≈
200 meV [7, 8] for LAO/STO sys-tems with similar Hall densities. Thus so far it has proved difficult engineer thesefundamental properties through control of the growth conditions. A direct compari-son of results from ARPES and transport experiments on a single STO 2DEG sam-ple could provide more insight and help to establish the extent to which electronicproperties can be considered universal. However, this remains a challenging task asthe surface 2DEG is not accessible to standard magneto-transport experiments whileARPES experiments on interfaces are limited to the soft X-ray regime where the ef-fective resolution has so far precluded results that resolve the full subband structure.In this regard, the aluminium oxide/STO interface studied by ARPES in Ref. [82]provides an interesting opportunity to overcome these difficulties as it is much moreamenable to magneto-transport experiments than the bare STO surface due to theprotective nature of the aluminium oxide over-layer.Another aspect that has perhaps not received the attention it deserves is the rela-tion between sample environment and 2DEG properties. In section 2.1 we describedthe exceptional sensitivity of the cleaved STO (001) surface to light induced oxygenvacancy formation as well as to the residual oxygen partial pressure. Adsorbates onthe LAO surface and irradiation even with visible light were also found to stronglyaffect the LAO/STO interface 2DEG [95, 89, 9]. Yet, the understanding of the ef-fects of different sample preparations and environments including electron and pho-ton beams, as they are used in many experiments, is only in its infancy and muchwork remains to be done to improve the consistency of experiments and ultimatelythe stability of devices. On the other hand, the sensitivity of emergent properties inoxides to defects, including those introduced by experimental probes, offers entirelynew perspectives for tailoring properties on the nanoscale [15, 18, 65].
Acknowledgements
The authors acknowledge financial support through the University of Genevaand the Swiss National Science Foundation and would like to thank C. Bernhard, R. Claessen, A.Fˆete, S. Gariglio, K. Held, P.D.C. King, F. Lechermann, L.D. Marks, W. Meevasana, N.C. Plumb,M. Radovic, V. Strocov, A. Tamai, J.M. Triscone, D. van der Marel and Z. Wang for discussions.
References
1. Y. Aiura, I. Hase, H. Bando, T. Yasue, T. Saitoh, and D. S. Dessau. Photoemission study ofthe metallic state of lightly electron-doped SrTiO . Surface Science , 515:61–74, 2002.2. M. Altmeyer, H. O. Jeschke, O. Hijano-Cubelos, C. Martins, F. Lechermann, K. Koepernik,A. F. Santander-Syro, M. J. Rozenberg, R. Valent´ı, and M. Gabay. Magnetism, Spin Tex-ture, and In-Gap States: Atomic Specialization at the Surface of Oxygen-Deficient SrTiO . Physical Review Letters , 116:157203, 2016.3. A. Annadi, Q. Zhang, X. Renshaw Wang, N. Tuzla, K. Gopinadhan, W. M. L¨u, A. RoyBarman, Z. Q. Liu, A. Srivastava, S. Saha, Y. L. Zhao, S. W. Zeng, S. Dhar, E. Olsson, B. Gu,S. Yunoki, S. Maekawa, H. Hilgenkamp, T. Venkatesan, and Ariando. Anisotropic two-6 Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumbergerdimensional electron gas at the LaAlO3/SrTiO3 (110) interface.
Nature Communications ,4:1838, 2013.4. M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan,Ph. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger. Emergent quantum confinement attopological insulator surfaces.
Nature Communications , 3:1159, 2012.5. C. Bareille, F. Fortuna, T. C. R¨odel, F. Bertran, M. Gabay, O. H. Cubelos, A. Taleb-Ibrahimi,P. Le F`evre, M. Bibes, A. Barth´el´emy, T. Maroutian, P. Lecoeur, M. J. Rozenberg, and A. F.Santander-Syro. Two-dimensional electron gas with six-fold symmetry at the (111) surfaceof KTaO3.
Scientific Reports , 4:3586, 2014.6. M. Basletic, J.-L. Maurice, C. Carr´et´ero, G. Herranz, O. Copie, M. Bibes, E. Jacquet,K. Bouzehouane, S. Fusil, and A. Barth´el´emy. Mapping the spatial distribution of chargecarriers in LaAlO /SrTiO heterostructures. Nature Materials , 7:621–625, 2008.7. G. Berner, S. Glawion, J. Walde, F. Pfaff, H. Hollmark, L.-C. Duda, S. Paetel, C. Richter,J. Mannhart, M. Sing, and R. Claessen. LaAlO /SrTiO oxide heterostructures studied byresonant inelastic x-ray scattering. Physical Review B , 82:241405, 2010.8. H. Boschker, C. Richter, E. Fillis-Tsirakis, C. W. Schneider, and J. Mannhart. Electron-phonon Coupling and the Superconducting Phase Diagram of the LaAlO -SrTiO Interface.
Scientific Reports , 5:12309, 2015.9. K. A. Brown, S. He, D. J. Eichelsdoerfer, M. Huang, I. Levy, H. Lee, S. Ryu, P. Irvin,J. Mendez-Arroyo, C.-B. Eom, C. A. Mirkin, and J. Levy. Giant conductivity switching ofLaAlO3/SrTiO3 heterointerfaces governed by surface protonation.
Nature Communications ,7:10681, 2016.10. Y. A. Bychkov and E. I. Rashba. Properties of a 2D electron gas with lifted spectral degen-eracy.
JETP Letters , 39:78–81, 1984.11. C. Cancellieri, A. S. Mishchenko, U. Aschauer, A. Filippetti, C. Faber, O. S. Barisic,V. A. Rogalev, T. Schmitt, N. Nagaosa, and V. N. Strocov. Polaronic metal state at theLaAlO /SrTiO interface. Nature Communications , 7:10386, 2016.12. C. Cancellieri, M. L. Reinle-Schmitt, M. Kobayashi, V. N. Strocov, T. Schmitt, P. R. Will-mott, S. Gariglio, and J.-M. Triscone. Interface Fermi States of LaAlO /SrTiO and RelatedHeterostructures. Physical Review Letters , 110:137601, 2013.13. A. D. Caviglia, M. Gabay, S. Gariglio, N. Reyren, C. Cancellieri, and J.-M. Triscone. TunableRashba Spin-Orbit Interaction at Oxide Interfaces.
Physical Review Letters , 104:126803,2010.14. A. D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Ham-merl, J. Mannhart, and J.-M. Triscone. Electric field control of the LaAlO /SrTiO interfaceground state. Nature , 456:624–627, 2008.15. C. Cen, S. Thiel, G. Hammerl, C. W. Schneider, K. E. Andersen, C. S. Hellberg, J. Mannhart,and J. Levy. Nanoscale control of an interfacial metal-insulator transition at room tempera-ture.
Nature Materials , 7:298–302, 2008.16. Y. J. Chang, A. Bostwick, Y. S. Kim, K. Horn, and E. Rotenberg. Structure and correlationeffects in semiconducting SrTiO . Physical Review B , 81:235109, 2010.17. C. Chen, J. Avila, E. Frantzeskakis, A. Levy, and M. C. Asensio. Observation of a two-dimensional liquid of Fr¨ohlich polarons at the bare SrTiO3 surface.
Nature Communications ,6:8585, 2015.18. G. Cheng, M. Tomczyk, S. Lu, J. P. Veazey, M. Huang, P. Irvin, S. Ryu, H. Lee, C.-B. Eom,C. S. Hellberg, and J. Levy. Electron pairing without superconductivity.
Nature , 521:196–199, 2015.19. O. Copie, V. Garcia, C. B¨odefeld, C. Carr´et´ero, M. Bibes, G. Herranz, E. Jacquet, J.-L.Maurice, B. Vinter, S. Fusil, K. Bouzehouane, H. Jaffr`es, and A. Barth´el´emy. TowardsTwo-Dimensional Metallic Behavior at LaAlO /SrTiO Interfaces.
Physical Review Letters ,102:216804, 2009.20. P. Delugas, V. Fiorentini, A. Mattoni, and A. Filippetti. Intrinsic origin of two-dimensionalelectron gas at the (001) surface of SrTiO . Physical Review B , 91:115315, 2015.21. J. T. Devreese and Alexandre S. Alexandrov. Fr¨ohlich polaron and bipolaron: recent devel-opments.
Reports on Progress in Physics , 72:066501, 2009.RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 2722. J. T. Devreese, S. N. Klimin, J. L. M. van Mechelen, and D. van der Marel. Many-body largepolaron optical conductivity in Nb:SrTiO . Physical Review B , 81:125119, 2010.23. U. Diebold. The surface science of titanium dioxide.
Surf. Sci. Rep. , 48:53–229, 2003.24. W. E. Doennig, D.and Pickett and R. Pentcheva. Massive Symmetry Breaking inLaAlO /SrTiO (111) Quantum Wells: A Three-Orbital Strongly Correlated Generalizationof Graphene. Physical Review Letters , 111:126804, 2013.25. A. Dubroka, M. R¨ossle, K. W. Kim, V. K. Malik, L. Schultz, S. Thiel, C. W. Schneider,J. Mannhart, G. Herranz, O. Copie, M. Bibes, A. Barth´el´emy, and C. Bernhard. DynamicalResponse and Confinement of the Electrons at the LaAlO /SrTiO Interface.
Physical ReviewLetters , 104:156807, 2010.26. L. Dudy, M. Sing, P. Scheiderer, J. D. Denlinger, P. Sch¨utz, J. Gabel, M. Buchwald,C. Schlueter, T.-l. Lee, and R. Claessen. In Situ Control of Separate Electronic Phases onSrTiO3 Surfaces by Oxygen Dosing.
Advanced Materials , 28:7443–7449, 2016.27. J. M. Edge, Y. Kedem, U. Aschauer, N. A. Spaldin, and A. V. Balatsky. Quantum CriticalOrigin of the Superconducting Dome in SrTiO . Physical Review Letters , 115:247002, 2015.28. A. Fˆete.
Magnetotransport experiments at the LaAlO /SrTiO interface . PhD thesis, Univer-sity of Geneva, 24 Quai Ernest-Ansermet, Geneva, CH-1211, Switzerland, 2014.29. A. Fˆete, C. Cancellieri, D. Li, D. Stornaiuolo, A. D. Caviglia, S. Gariglio, and J.-M. Triscone.Growth-induced electron mobility enhancement at the LaAlO /SrTiO interface. AppliedPhysics Letters , 106:051604, 2015.30. A. Fˆete, S. Gariglio, C. Berthod, D. Li, D. Stornaiuolo, M. Gabay, and J.-M. Triscone.Large modulation of the Shubnikov–de Haas oscillations by the Rashba interaction at theLaAlO /SrTiO interface. New Journal of Physics , 16:112002, 2014.31. A. Fˆete, S. Gariglio, A. D. Caviglia, J.-M. Triscone, and M. Gabay. Rashba induced mag-netoconductance oscillations in the LaAlO -SrTiO heterostructure. Physical Review B ,86:201105(R), 2012.32. L. Forro, O. Chauvet, D. Emin, L. Zuppiroli, H. Berger, and F. L´evy. High mobility ntypecharge carriers in large single crystals of anatase (tio2).
Journal of Applied Physics , 75:633–635, 1994.33. A. C. Garcia-Castro, M. G. Vergniory, E. Bousquet, and A. H. Romero. Spin texture in-duced by oxygen vacancies in strontium perovskite (001) surfaces: A theoretical comparisonbetween SrTiO and SrHfO . Physical Review B , 93:045405, 2016.34. S. Gariglio, A. Fˆete, and J.-M. Triscone. Electron confinement at the LaAlO /SrTiO inter-face. Journal of Physics: Condensed Matter , 27:283201, 2015.35. L. P. Gor’kov. Phonon mechanism in the most dilute superconductor: n -type SrTiO . Pro-ceedings of the National Academy of Sciences of the United States of America , 113:4646–4651, 2015.36. V. E. Henrich, G. Dresselhaus, and H. J. Zeiger. Surface defects and the electronic structureof SrTi O3 surfaces.
Physical Review B , 17:4908–4921, 1978.37. G. Herranz, F. S´anchez, N. Dix, M. Scigaj, and J. Fontcuberta. High mobility conduction at(110) and (111) LaAlO /SrTiO interfaces. Scientific Reports , 2:758, 2012.38. S. Hurand, A. Jouan, C. Feuillet-Palma, G. Singh, J. Biscaras, E. Lesne, N. Reyren,A. Barth´el´emy, M. Bibes, J. E. Villegas, C. Ulysse, X. Lafosse, M. Pannetier-Lecoeur,S. Caprara, M. Grilli, J. Lesueur, and N. Bergeal. Field-effect control of superconductiv-ity and Rashba spin-orbit coupling in top-gated LaAlO /SrTiO devices. Scientific Reports ,5:12751, 2015.39. M. Itoh and R. Wang. Quantum ferroelectricity in SrTiO induced by oxygen isotope ex-change. Applied Physics Letters , 76:221, 2000.40. J. Ja´cimovi´c, R. Ga´al, A. Magrez, J. Piatek, L. Forr´o, L., S. Nakao, Y. Hirose, andT. Hasegawa. Low temperature resistivity, thermoelectricity, and power factor of Nb dopedanatase TiO . Applied Physics Letters , 102:013901, 2013.41. R. Jany, C. Richter, C. Woltmann, G. Pfanzelt, B. F¨org, M. Rommel, T. Reindl, U. Waizmann,J. Weis, J. A. Mundy, D. A. Muller, H. Boschker, and J. Mannhart. Monolithically IntegratedCircuits from Functional Oxides.
Advanced Materials Interfaces , 1:1300031, 2014.8 Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger42. H. O. Jeschke, J. Shen, and R. Valenti. Localized versus itinerant states created by multipleoxygen vacancies in SrTiO . New Journal of Physics , 17:023034, 2015.43. G. Khalsa, B. Lee, and A. H. MacDonald. Theory of t g electron-gas Rashba interactions. Physical Review B , 88:041302, 2013.44. M. Kim, C. Bell, Y. Kozuka, M. Kurita, Y. Hikita, and H. Y. Hwang. Fermi surface andsuperconductivity in low-density high-mobility δ -doped SrTiO . Physical Review Letters ,107:106801, 2011.45. P. Kim, K. T. Kang, G. Go, and J. H. Han. Nature of orbital and spin Rashba coupling in thesurface bands of SrTiO and KTaO . Physical Review B , 90:205423, 2014.46. Y. Kim, R. M. Lutchyn, and C. Nayak. Origin and transport signatures of spin-orbit in-teractions in one- and two-dimensional SrTiO -based heterostructures. Physical Review B ,87:245121, 2013.47. P. D. C. King, R. Hatch, M. Bianchi, R. Ovsyannikov, C. Lupulescu, G. Landolt, B. Slomski,J. H. Dil, D. Guan, J. Mi, E. Rienks, J. Fink, A. Lindblad, S. Svensson, S. Bao, G. Balakr-ishnan, B. Iversen, J. Osterwalder, W. Eberhardt, F. Baumberger, and P. Hofmann. LargeTunable Rashba Spin Splitting of a Two-Dimensional Electron Gas in Bi2Se3.
PhysicalReview Letters , 107:96802, 2011.48. P. D. C. King, R. H. He, T. Eknapakul, P. Buaphet, S.-K. Mo, Y. Kaneko, S. Harashima,Y. Hikita, M. S. Bahramy, C. Bell, Z. Hussain, Y. Tokura, Z.-X. Shen, H. Y. Hwang, F. Baum-berger, and W. Meevasana. Subband Structure of a Two-Dimensional Electron Gas Formedat the Polar Surface of the Strong Spin-Orbit Perovskite KTaO . Physical Review Letters ,108:117602, 2012.49. P. D. C. King, S. McKeown Walker, A. Tamai, A. de la Torre, T. Eknapakul, P. Buaphet,S.-K. Mo, W. Meevasana, M. S. Bahramy, and F. Baumberger. Quasiparticle dynamics andspin-orbital texture of the SrTiO two-dimensional electron gas. Nature Communications ,5:3414, 2014.50. P. D. C. King, T. Veal, and C. McConville. Nonparabolic coupled Poisson-Schr¨odinger solu-tions for quantized electron accumulation layers: Band bending, charge profile, and subbandsat InN surfaces.
Physical Review B , 77:125305, 2008.51. P. D. C. King, T. D. Veal, C. F. McConville, J. Z´u˜niga P´erez, V. Mu˜noz Sanjos´e, M. Hop-kinson, E. D. L. Rienks, M. F. Jensen, and P. Hofmann. Surface band-gap narrowing inquantized electron accumulation layers.
Physical Review Letters , 104:256803, 2010.52. P. D. C. King, H. I. Wei, Y. F. Nie, M. Uchida, C. Adamo, S. Zhu, X. He, I. Boˇzovi´c, D. G.Schlom, and K. M. Shen. Atomic-scale control of competing electronic phases in ultrathinLaNiO . Nature Nanotechnology , 9:443–447, 2014.53. M. L. Knotek. Stimulated desorption from surfaces.
Physics Today , 37:24, 1984.54. M. L. Knotek and P.J. Feibelman. Ion Desorption by Core-Hole Auger Decay.
PhysicalReview Letters , 40:964–967, 1978.55. H. C. Koo, J. H. Kwon, J. Eom, J. Chang, S. H. Han, and M. Johnson. Control of SpinPrecession in a Spin-Injected Field Effect Transistor.
Science , 325:1515–1518, 2009.56. S. LaShell, B. A. McDougall, and E. Jensen. Spin Splitting of an Au(111) Surface StateBand Observed with Angle Resolved Photoelectron Spectroscopy.
Physical Review Letters ,77:3419–3422, 1996.57. H. Liang, L. Cheng, L. Wei, Z. Luo, G. Yu, C. Zeng, and Z. Zhang. Nonmonotonically tun-able Rashba spin-orbit coupling by multiple-band filling control in SrTiO -based interfacial d -electron gases. Physical Review B , 92:075309, 2015.58. C. Lin and A. A. Demkov. Electron Correlation in Oxygen Vacancy in SrTiO . PhysicalReview Letters , 111:217601, 2013.59. J. Mannhart and D. G. Schlom. Oxide Interfaces–An Opportunity for Electronics.
Science ,327:1607–1611, 2010.60. A. McCollam, S. Wenderich, M. K. Kruize, V. K. Guduru, H. J. A Molegraaf, M. Huijben,G. Koster, D. H a Blank, G. Rijnders, A. Brinkman, H. Hilgenkamp, U. Zeitler, and J. C.Maan. Quantum oscillations and subband properties of the two-dimensional electron gas atthe LaAlO /SrTiO interface. APL Materials , 2:022102, 2014.RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 2961. S. McKeown Walker.
Two Dimensional Electron Liquids at Oxide Surfaces Studied by AngleResolved Photoemission Spectroscopy . PhD thesis, University of Geneva, 24 Quai Ernest-Ansermet, Geneva, CH-1211, Switzerland, 2016.62. S. McKeown Walker, F. Y. Bruno, Z. Wang, A. de la Torre, S. Ricc´o, A. Tamai, T. K. Kim,M. Hoesch, M. Shi, M. S. Bahramy, P. D. C. King, and F. Baumberger. Carrier-Density Con-trol of the SrTiO (001) Surface 2D Electron Gas studied by ARPES. Advanced Materials ,27:3894–3899, 2015.63. S. McKeown Walker, A. de la Torre, F. Y. Bruno, A. Tamai, T. K. Kim, M. Hoesch, M. Shi,M. S. Bahramy, P. D. C. King, and F. Baumberger. Control of a Two-Dimensional ElectronGas on SrTiO3(111) by Atomic Oxygen.
Physical Review Letters , 113:177601, 2014.64. S. McKeown Walker, S. Ricc`o, F. Y. Bruno, A. de la Torre, A. Tamai, E. Golias,A. Varykhalov, D. Marchenko, M. Hoesch, M. S. Bahramy, P. D. C. King, J. S´anchez-Barriga,and F. Baumberger. Absence of giant spin splitting in the two-dimensional electron liquid atthe surface of SrTiO (001). Physical Review B , 93:245143, 2016.65. W. Meevasana, P. D. C. King, R. H. He, S.-K. Mo, M. Hashimoto, A. Tamai, P. Songsiririt-thigul, F. Baumberger, and Z.-X. Shen. Creation and control of a two-dimensional electronliquid at the bare SrTiO surface. Nature Materials , 10:114–118, 2011.66. W. Meevasana, X. J. Zhou, B. Moritz, C.-C. Chen, R. H. He, S.-I. Fujimori, D. H. Lu, S.-K.Mo, R .G. Moore, F. Baumberger, T. P. Devereaux, D. van der Marel, N. Nagaosa, J. Zaanen,and Z.-X. Shen. Strong energy-momentum dispersion of phonon-dressed carriers in thelightly doped band insulator SrTiO . New Journal of Physics , 12:023004, 2010.67. E. Mikheev, B. Himmetoglu, A. P. Kajdos, P. Moetakef, T. A. Cain, C. G. Van De Walle, andS. Stemmer. Limitations to the room temperature mobility of two- and three-dimensionalelectron liquids in SrTiO . Applied Physics Letters , 106:062102, 2015.68. M. Minohara, T. Tachikawa, Y. Nakanishi, Y. Hikita, L. F. Kourkoutis, J.-S. Lee, C.-C. Kao,M. Yoshita, H. Akiyama, C. Bell, and H. Y. Hwang. Atomically Engineered Metal–InsulatorTransition at the TiO /LaAlO Heterointerface.
Nano Letters , 14:6743–6746, 2014.69. A. S. Mishchenko, N. V. Prokofev, A. Sakamoto, and B. V. Svistunov. Diagrammatic quan-tum Monte Carlo study of the Fr¨ohlich polaron A.
Physical Review B , 62:6317–6336, 2000.70. P. Moetakef, D. G. Ouellette, J. R. Williams, S. James Allen, L. Balents, D. Goldhaber-Gordon, and S. Stemmer. Quantum oscillations from a two-dimensional electron gas at aMott/band insulator interface.
Applied Physics Letters , 101:151604, 2012.71. S. Moser, L. Moreschini, J. Ja´cimovi´c, O. S. Bariˇsi´c, H. Berger, A. Magrez, Y. J. Chang, K. S.Kim, a. Bostwick, E. Rotenberg, L. Forr´o, and M. Grioni. Tunable Polaronic Conduction inAnatase TiO . Physical Review Letters , 110:196403, 2013.72. H. Nakamura and T. Kimura. Electric field tuning of spin-orbit coupling in KTaO field-effect transistors. Physical Review B , 80:121308(R), 2009.73. H. Nakamura, T. Koga, and T. Kimura. Experimental Evidence of Cubic Rashba Effect in anInversion-Symmetric Oxide.
Physical Review Letters , 108:206601, 2012.74. J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki. Gate Control of Spin-Orbit Interac-tion in an Inverted In . Ga . As/In . Al . As heterostructure .
Physical Review Letters ,78:1335–1338, 1997.75. I. Pallecchi, F. Telesio, D. Li, A. Fˆete, S. Gariglio, J.-M. Triscone, A. Filippetti, P. Delugas,V. Fiorentini, and D. Marr´e. Giant oscillating thermopower at oxide interfaces.
NatureCommunications , 6:6678, 2015.76. L. F. J. Piper, L. Colakerol, P. D. C. King, A. Schleife, J. Z´u˜niga P´erez, P. A. Glans, T. Lear-month, A. Federov, T. D. Veal, F. Fuchs, V. Mu˜noz Sanjos´e, F. Bechstedt, C. F. McConville,and K. E. Smith. Observation of quantized subband states and evidence for surface electronaccumulation in CdO from angle-resolved photoemission spectroscopy.
Physical Review B ,78:165127, 2008.77. N. C. Plumb, M. Salluzzo, E. Razzoli, M. M˚ansson, M. Falub, J. Krempasky, C.E. Matt,J. Chang, M. Schulte, J. Braun, H. Ebert, J. Min´ar, B. Delley, K.-J. Zhou, T. Schmitt, M. Shi,J. Mesot, L. Patthey, and M. Radovi´c. Mixed Dimensionality of Confined Conducting Elec-trons in the Surface Region of SrTiO . Physical Review Letters , 113:086801, 2014.0 Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger78. S. Raghavan, J. Y. Zhang, and S. Stemmer. Two-dimensional electron liquid at the (111)SmTiO /SrTiO interface. Applied Physics Letters , 106:132104, 2015.79. N. Reyren, S. Gariglio, A. D. Caviglia, D. Jaccard, T. Schneider, and J.-M. Triscone.Anisotropy of the superconducting transport properties of the LaAlO /SrTiO interface. Ap-plied Physics Letters , 94:112506, 2009.80. T. C. R¨odel, C. Bareille, F. Fortuna, C. Baumier, F. Bertran, P. Le F`evre, M. Gabay, O. HijanoCubelos, M. J. Rozenberg, T. Maroutian, P. Lecoeur, and A.F. Santander-Syro. OrientationalTuning of the Fermi Sea of Confined Electrons at the SrTiO . Physical Review Applied ,1:051002, 2014.81. T. C. R¨odel, F. Fortuna, F. Bertran, M. Gabay, M. J. Rozenberg, A. F. Santander-Syro, andP. Le F`evre. Engineering two-dimensional electron gases at the (001) and (101) surfaces ofTiO anatase using light. Physical Review B , 92:041106(R), 2015.82. T. C. R¨odel, F. Fortuna, S. Sengupta, E. Frantzeskakis, Patrick Le F`evre, F. Bertran, B. Mer-cey, S. Matzen, G. Agnus, T. Maroutian, P. Lecoeur, and A. F. Santander-Syro. UniversalFabrication of 2D Electron Systems in Functional Oxides.
Advanced Materials , 28:1976–1980, 2016.83. S. E. Rowley, L. J. Spalek, R. P. Smith, M. P. M. Dean, M. Itoh, J. F. Scott, G. G. Lonzarich,and S. S. Saxena. Ferroelectric quantum criticality.
Nature Physics , 10:367–372, 2014.84. M. Salluzzo, J. C. Cezar, N. B. Brookes, V. Bisogni, G. M. De Luca, C. Richter, S. Thiel,J. Mannhart, M. Huijben, A. Brinkman, G. Rijnders, and G. Ghiringhelli. Orbital Recon-struction and the Two-Dimensional Electron Gas at the LaAlO /SrTiO Interface.
PhysicalReview Letters , 102:166804, 2009.85. A. F. Santander-Syro, C. Bareille, F. Fortuna, O. Copie, M. Gabay, F. Bertran, A. Taleb-Ibrahimi, P. Le F`evre, G. Herranz, N. Reyren, M. Bibes, A. Barth´el´emy, P. Lecoeur, J. Gue-vara, and M. J. Rozenberg. Orbital symmetry reconstruction and strong mass renormal-ization in the two-dimensional electron gas at the surface of KTaO . Physical Review B ,86:121107(R), 2012.86. A. F. Santander-Syro, O. Copie, T. Kondo, F. Fortuna, S. Pailh`es, R. Weht, X. G. Qiu,F. Bertran, A. Nicolaou, A. Taleb-Ibrahimi, P. Le F`evre, G. Herranz, M. Bibes, N. Reyren,Y. Apertet, P. Lecoeur, A. Barth´el´emy, and M. J. Rozenberg. Two-dimensional electron gaswith universal subbands at the surface of SrTiO . Nature , 469:189–193, 2011.87. A. F. Santander-Syro, F. Fortuna, C. Bareille, T. C. R¨odel, G. Landolt, N. C. Plumb, J. H.Dil, and M. Radovi´c. Giant spin splitting of the two-dimensional electron gas at the surfaceof SrTiO . Nature Materials , 13:1085–1090, 2014.88. T. Sarkar, K. Gopinadhan, J. Zhou, S. Saha, J. M. D. Coey, Y. Pi. Feng, Ariando, andT. Venkatesan. Electron Transport at the TiO Surfaces of Rutile, Anatase, and Stron-tium Titanate: The Influence of Orbital Corrugation.
ACS Applied Materials and Interfaces ,7(44):24616, 2015.89. P. Scheiderer, F. Pfaff, J. Gabel, M. Kamp, M. Sing, and R. Claessen. Surface-interfacecoupling in an oxide heterostructure: Impact of adsorbates on LaAlO /SrTiO . PhysicalReview B , 92:195422, 2015.90. J. Schooley, W. Hosler, E. Ambler, J. Becker, M. Cohen, and C. Koonce. Dependence ofthe Superconducting Transition Temperature on Carrier Concentration in SemiconductingSrTiO . Physical Review Letters , 14:305–307, 1965.91. K. V. Shanavas. Theoretical study of the cubic Rashba effect at the SrTiO (001) surfaces. Physical Review B , 93:045108, 2016.92. M. Sing, G. Berner, K. Goß, A. M¨uller, A. Ruff, A. Wetscherek, S. Thiel, J. Mannhart, S. A.Pauli, C. W. Schneider, P. R. Willmott, M. Gorgoi, F. Sch¨afers, and R. Claessen. Profilingthe interface electron gas of LaAlO /SrTiO heterostructures with hard x-ray photoelectronspectroscopy. Physical Review Letters , 102:176805, 2009.93. A. Spinelli, M. A. Torija, C. Liu, C. Jan, and C. Leighton. Electronic transport in dopedSrTiO : Conduction mechanisms and potential applications. Physical Review B , 81:155110,2010.94. M. Stengel. First-Principles Modeling of Electrostatically Doped Perovskite Systems.
Phys-ical Review Letters , 106:136803, 2011.RPES Studies of Two-Dimensional Electron Gases at Transition Metal Oxide Surfaces 3195. A. Tebano, E. Fabbri, D. Pergolesi, G. Balestrino, and E. Traversa. Room-temperature giantpersistent photoconductivity in SrTiO /LaAlO heterostructures. ACS Nano , 6:1278–1283,2012.96. Y. Tokura, Y. Taguchi, Y. Okada, Y. Fujishima, T. Arima, K. Kumagai, and Y. Iye. Fill-ing dependence of electronic properties on the verge of metal-Mott-insulator transition inSr − x La x TiO . Physical Review Letters , 70:2126, 1993.97. K. Ueno, S. Nakamura, H. Shimotani, H. T. Yuan, N. Kimura, T. Nojima, H. Aoki, Y. Iwasa,and M. Kawasaki. Discovery of superconductivity in KTaO by electrostatic carrier doping. Nature Nanotechnology , 6:408–412, 2011.98. H. Uwe, J. Kinoshita, K. Yoshihiro, C. Yamanouchi, and T. Sakudo. Evidence for light andheavy conduction electrons at the zone center in KTaO . Physical Review B , 19:3041–3044,1979.99. D. van der Marel, J. L. M. van Mechelen, and I. I. Mazin. Common Fermi-liquid origin ofT resistivity and superconductivity in n-type SrTiO . Physical Review B , 84:205111, 2011.100. L. W. van Heeringen, G. A. De Wijs, A. McCollam, J. C. Maan, and A. Fasolino. k · p subband structure of the LaAlO /SrTiO interface. Physical Review B , 88:205104, 2013.101. J. L. M. van Mechelen, D. van der Marel, C. Grimaldi, A. Kuzmenko, N. Armitage,N. Reyren, H. Hagemann, and I. Mazin. Electron-Phonon Interaction and Charge CarrierMass Enhancement in SrTiO . Physical Review Letters , 100:226403, 2008.102. G. Verbist, F. M. Peeters, and J. T. Devreese. Extended stability region for large bipolaronsthrough interaction with multiple phonon branches.
Ferroelectrics , 130:27–34, 1992.103. Z. Wang, S. McKeown Walker, A. Tamai, Y. Wang, Z. Ristic, F. Y. Bruno, A. de la Torre,S. Ricc`o, N. C. Plumb, M. Shi, P. Hlawenka, J. S´anchez-Barriga, A. Varykhalov, T. K. Kim,M. Hoesch, P. D. C. King, W. Meevasana, U. Diebold, J. Mesot, B. Moritz, T. P. Devereaux,M. Radovic, and F. Baumberger. Tailoring the nature and strength of electron–phonon inter-actions in the SrTiO (001) 2D electron liquid. Nature Materials , 15:835–839, 2016.104. Z. Wang, Z. Zhong, X. Hao, S. Gerhold, B. St¨oger, M. Schmid, J. S´anchez-Barriga,A. Varykhalov, C. Franchini, K. Held, and U. Diebold. Anisotropic two-dimensional electrongas at SrTiO3(110).
Proceedings of the National Academy of Sciences of the United Statesof America , 111:3933–3937, 2014.105. Z. Wang, Z. Zhong, S. McKeown Walker, Z. Ristic, J.-Z. Ma, F. Y. Bruno, S. Ricc`o, G. San-giovanni, G. Eres, N.C. Plumb, L. Patthey, M. Shi, J. Mesot, F. Baumberger, and M. Radovi´c.Atomically precise lateral modulation of a two-dimensional electron liquid in anatase TiO thin films. Submitted , 2016.106. S. H. Wemple. Some Transport Properties of Oxygen-Deficient Single-Crystal PotassiumTantalate (KTaO ). Physical Review , 137:A1575, 1965.107. Roland Winkler.
Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Sys-tems . Springer-Verlag Berlin Heidelberg, 2003.108. D. Xiao, W. Zhu, Y. Ran, N. Nagaosa, and S. Okamoto. Interface engineering of quantumHall effects in digital transition metal oxide heterostructures.
Nature Communications , 2:596,2011.109. K. Yoshimatsu, T. Okabe, H. Kumigashira, S. Okamoto, S. Aizaki, A. Fujimori, and M. Os-hima. Dimensional-crossover-driven metal-insulator transition in srvo ultrathin films. Phys-ical Review Letters , 104:147601, 2010.110. R. Yukawa, K. Ozawa, S. Yamamoto, R.-Y. Liu, and I. Matsuda. Anisotropic effective massapproximation model to calculate multiple subband structures at wide-gap semiconductorsurfaces: Application to accumulation layers of SrTiO and ZnO. Surface Science , 641:224–230, 2015.111. K. H. L. Zhang, R. G. Egdell, F. Offi, S. Iacobucci, L. Petaccia, S. Gorovikov, and P. D. C.King. Microscopic origin of electron accumulation in In2O3.
Physical Review Letters ,110:056803, 2013.112. Z. Zhong, A. T´oth, and K. Held. Theory of spin-orbit coupling at LaAlO /SrTiO interfacesand SrTiO surfaces. Physical Review B , 87:161102, 2013.2 Siobhan McKeown Walker and Flavio Y. Bruno and Felix Baumberger113. J. Zhou, W. Y. Shan, and D. Xiao. Spin responses and effective Hamiltonian for thetwo-dimensional electron gas at the oxide interface LaAlO / SrTiO . Physical Review B ,91:241302(R), 2015.114. K.-Ji. Zhou, M. Radovic, J. Schlappa, V. Strocov, R. Frison, J. Mesot, L. Patthey, andT. Schmitt. Localized and delocalized Ti 3 d carriers in LaAlO /SrTiO superlattices revealedby resonant inelastic x-ray scattering. Physical Review B , 83:201402(R), 2011.115. K. Zou, S. Ismail-Beigi, K. Kisslinger, X. Shen, D. Su, F. J. Walker, and C. H. Ahn.LaTiO /KTaO interfaces: A new two-dimensional electron gas system. APL Materials ,3:036104, 2015.116. P. Zubko, S. Gariglio, P. Gabay, M.and Ghosez, and J.-M. Triscone. Interface Physics inComplex Oxide Heterostructures.