Rashba split surface states in BiTeBr
aa r X i v : . [ c ond - m a t . m t r l - s c i ] F e b Rashba split surface states in BiTeBr
S. V. Eremeev,
1, 2
I. P. Rusinov, I. A. Nechaev,
2, 3 and E. V. Chulkov
3, 4, 5 Institute of Strength Physics and Materials Science, 634021, Tomsk, Russia Tomsk State University, 634050, Tomsk, Russia Donostia International Physics Center (DIPC),20018 San Sebasti´an/Donostia, Basque Country, Spain Departamento de F´ısica de Materiales UPV/EHU,Facultad de Ciencias Qu´ımicas, UPV/EHU, Apdo. 1072,20080 San Sebasti´an/Donostia, Basque Country, Spain Centro de F´ısica de Materiales CFM - MPC, Centro Mixto CSIC-UPV/EHU,20080 San Sebasti´an/Donostia, Basque Country, Spain (Dated: October 29, 2018)Within density functional theory, we study bulk band structure and surface states of BiTeBr.We consider both ordered and disordered phases which differ in atomic order in the Te-Br sub-lattice. On the basis of relativistic ab-initio calculations, we show that the ordered BiTeBr isenergetically preferable as compared with the disordered one. We demonstrate that both Te- andBr-terminated surfaces of the ordered BiTeBr hold surface states with a giant spin-orbit splitting.The Te-terminated surface-state spin splitting has the Rashba-type behavior with the coupling pa-rameter α R ∼ PACS numbers: 73.20.-r, 75.70.Tj
INTRODUCTION
Nowadays, a controllable manipulation of the elec-tronic spin degree-of-freedom without recourse to an ex-ternal magnetic field is a process in technological de-mand, since it constitutes the basis of functionality ofspintronics devices [1]. An obvious candidate for the phe-nomenon underlying this process is spin-orbit interaction(SOI) that couples spin and momentum of electrons. Inthe case of two-dimensional (2D) geometries (surfaces,asymmetric quantum wells, etc.), the SOI may result in aspin splitting of electron states, which has a nature of theso-called Rashba effect [2]. This splitting can be tunedby an applied electric field [3–7], which opens a pathwayfor realizing electric-field spin manipulation. There aretwo key operating characteristics here: the Rashba en-ergy, E R , and the momentum offset of split states, k R ,which together define the Rashba coupling strength as α R = 2 E R /k R .In the conventional semiconductor structures, wherethe Rashba effect has been revealed for the first time,the parameter α R is of order of 10 − eV˚A (see, e.g.,Refs. [4, 8, 9]). However, for room-temperature appli-cations of spintronics devices, it is crucial to have α R as large as possible. As a result, over a long period oftime the Rashba effect keeps attracting a great inter-est, and many systems with a large Rashba spin splittinghave been discovered. It was found that the ¯Γ surfacestate on Au(111) has a Rashba splitting with α R that isabout five times larger than that in the semiconductorheterostructures (see, e.g., Refs. [10–12]). A larger α R (half as much as that for Au(111)) has been reported fora surface state at the Bi(111) surface [13]. In seeking away to tune spin-orbit-splitting of surface states, it was shown that, for instance, in the case of the Au(111) sur-face it can be done with deposition of Ag-atoms [14, 15].As was demonstrated in Refs. [16–22], a more effectiveway to modify spin splitting of surface states is a surfacealloying of heavy elements (Bi, Pb, Sb) on noble-metalsurfaces. In this case, one arrives at a Rashba-type splitsurface state with α R that is about one order of magni-tude greater than that in the semiconductor structures.To go further in possible tuning of spin-orbit-splittingof electron states, quantum-well states evolving by theconfinement of electrons in ultrathin metal films havebeen considered. In the presence of both the surface andthe interface with a substrate, a number of impacts on thesplitting doubles. As was reported, e.g., in Ref. [23], a Bimonolayer film on Cu(111) can provide with spin-orbit-split quantum-well states in the unoccupied electronicstructure, which are characterized by α R similar to thatin the surface alloys. However, apart from a large spin-orbit splitting, for an efficient spintronics application inthe way specified above a semiconductor substrate andthe absence of spin-degenerate carriers in a quite wideenergy interval are more promising.In the case of semiconductor substrate (e.g., an ul-trathin Pb films on Si(111) [24]) quantum well statesshow a Rashba splitting as small as in the semicon-ductor structures. A large Rashba spin splitting on asemiconductor substrate can be reached, for example, bymeans of a Bi-trimer adlayer on a Si(111) surface (seealso Ref. [25]), where the splitting has a similar originas in the Bi/Ag(111) surface alloy and a close value forthe parameter α R [26]. Nevertheless, the found spin-split2D states cannot be well described by a simple Rashbamodel, where a parabolic dispersion with a positive effec-tive mass combines with the spin-splitting that is linearin electron momentum. This motivates an active searchof new materials and a revision of the already known sys-tems with a SOI that under certain conditions can leadto a technologically meaningful spin spliting of a free-electron-like state at a semiconductor surface. In thatsense, the reexamining of bismuth tellurohalides, wherea Rashba-type spin splitting of states has been revealedto be caused by intrinsic inversion asymmetry of bulkcrystal potential [27, 28], can be considered as a greatadvance made recently in the search. Actually, it wasshown that Te-terminated surfaces of BiTeCl and BiTeIpossess a giant spin-orbit splitting of a free-electron-likesurface state [29–32].The mentioned bismuth tellurohalides have hexago-nal crystal structures [33] and are characterized by ionicbonding with large charge transfer from Bi to halide- andTe-atomic layers. The crystal structure is built up of al-ternating hexagonal layers Te-Bi-I(Cl) stacked along thehexagonal axis. Besides, each three layers Te-Bi-I(Cl)form a three-layer (TL) block, and the distance betweenthe blocks is about one and a half times greater thanthe interlayer distances within the Te-Bi-I(Cl) TL struc-ture. Such a three-layered structure breaks the inver-sion symmetry of bulk crystal potential, which leads toappearing of the Rashba-type spin-orbit splitting of thebulk bands [27]. Due to the layered crystal structure, thebismuth tellurohalide surfaces can be terminated by Te-or halide-atom-layer. Both these terminations hold spin-split surface states [29–32]. These states emerge by split-ting off either from the lowest conduction band (for theTe-termination) or from the uppermost valence band (forthe halide-atom-termination). The splitting off is causedby changes in potential (decreasing at the Te-terminatedsurface and increasing at the halide-atom-terminated sur-face) within the near-surface layers [29] as compared withthe bulk region, which is a consequence of strong ionicity.In addition to BiTeCl and BiTeI, the bismuth-tellurohalide group is known to have one moresemiconductor—BiTeBr. It was previously reported[33, 34] that its layered crystal structure is a disor-dered centrosymmetric one, where tellurium and bromineatoms randomly distributed within two layers adjacent toBi-atomic layer [33, 34]. As a consequence, both the bulkand surface electronic structure of the disordered BiTeBrwas never addressed before. Recently, bulk electronicstructure of the ordered BiTeBr has been calculated andRashba-type splitting of some bands has been analyzed[29].In the present paper, we examine both disordered andordered phases of BiTeBr. We model the crystal struc-ture of the ordered phase as that of BiTeI but with Brinstead of I and the lattice parameters were taken formRef. [33], at that atomic positions are obtained within astructural optimization. On the basis of ab-initio calcula-tions we show that the ordered structure is energeticallypreferable. We demonstrate that both the Te- and Br- terminated surfaces of the ordered BiTeBr hold the spin-orbit split surface states emerged by splitting off from thebulk conduction or valence band like in other bismuthtellurohalides. For the practical use, as in the case ofBiTeCl and BiTeI the Te-terminated surface of BiTeBris more suitable than the halide-atom-terminated one,since it holds a surface state that has a free-electron-likedispersion and a large Rashba-type spin splitting. Atthe same time, BiTeBr has an advantage over BiTeCland BiTeI. As compared with BiTeCl, the bromide hasa larger Rashba spin splitting of the Te-terminated sur-face state and a wider bulk band gap. In contrast toBiTeI, the surface state is larger split off from the bulkconduction band and more isotropic. COMPUTATIONAL METHOD
The structural optimization and electronic band calcu-lations are performed within the density functional for-malism as implemented in
VASP [35, 36]. We use the all-electron projector augmented wave (PAW) [37, 38] basissets with the generalized gradient approximation (GGA)of Perdew, Burke, and Ernzerhof (PBE) [39] to the ex-change correlation (XC) potential. The Hamiltonian con-tains the scalar relativistic corrections, and the SOI wastaken into account by the second variation method [40].To treat the bulk disordered phase effect, we employtwo approaches. The first one is a supercell approachused within
VASP , where 4 × × ABINIT code [41], where the configuration averaged potential ofa gray atom occupying a site in the Te-Br sublattice isdefined as a mixture V VCA = xV Br + (1 − x ) V Te of Br( V Br ) and Te ( V Te ) pseudopotentials with x = 0 .
5. Weused GGA-PBE Hartwigsen-Goedecker-Hutter (HGH)[42] relativistic norm-conserving pseudopotentials takenfrom Ref. [43] which include the SOI.The surface of the ordered BiTeBr formed under cleav-age can have Te-layer or Br-layer termination. To sim-ulate semi-infinite BiTeBr(0001), using
VASP we con-sider a 24 atomic layer slab with bromine side (for Te-terminated surface) or tellurium side (for Br-terminatedsurface) passivated by hydrogen monolayer.
CALCULATION RESULTS AND DISCUSSION
In earlier works [33, 34], the CdI hexagonal struc-ture for BiTeBr was reported. This structure differs fromthat of BiTeI in that Br and Te atoms are statisticallydistributed over I -type sites (Fig. 1(a)). According toRef. [33], the mixed Te/Br layers are located at a dis-tance of ± FIG. 1: Atomic structure of BiTeBr: disordered structure astaken from Ref. [33] (a) and optimized ordered structure (b).FIG. 2: (a) Band structure calculated by the VASP alonghigh symmetry directions of the Brillouin zone for the BiTeBrordered phase, and (b) magnified view of the bulk elec-tronic structure in the vicinity of the A point calculated withuse both PAW (VASP) and pseudopotential (ABINIT) ap-proaches; inset in panel (b) shows the lowest conduction bandin the vicinity of the A point calculated within the 4 × × geometry of the disordered phase, we constructed a setof 4 × × ∼ . ∼ . ∼ k R that in A-H and A-L di-rections is of ∼ .
05 and 0 .
04 ˚A − for the VBM and theCBM, respectively. The Rashba energy for the VBM isapproximately twice of that for the CBM (111 meV vs 66meV). As a result, it provides noticeably larger spin-orbitcoupling for the upper valence-band states as comparedwith the lower conduction-band states (see Tabl. I).As seen in the Fig. 2(b), the pseudopotential ABINIT calculations performed for the ordered BiTeBr confirmthe large spin-orbit splitting in the vicinity of the A point.Moreover, we have obtained values for the Rashba pa-rameters, which are very close to those found with VASP(see α R in Tabl. I). The bulk band gap evaluated byABINIT is about 100 meV smaller than that obtainedfrom the VASP calculations. The spectrum calculatedwithin the VCA for the disordered phase shows practi-cally the same band gap and demonstrates the expectedlack of spin-splitting of the bulk bands due to the pres-ence of inversion symmetry in the disordered structure.Note that the spin-splitting of the bulk bands obtainedwithin supercell approach is negligible, and it agrees wellwith the VCA result (Fig. 2(b), inset), which indicatesthat chosen 4 × × V , in the near-surface lay- TABLE I: Rashba coupling parameters α R (eV˚A) for the bulkvalence and conduction bands in the vicinity of the A pointin the A-H and A-L directions. The calculated values for thebulk band gap, E g , are also presented. E g (meV) valence band conduction bandA-H A-L A-H A-L VASP
283 4.33 4.36 3.52 3.57
ABINIT
187 4.72 4.93 3.97 4.06FIG. 3: The change of the potential in the near-surface layersof the crystal with respect to that in the central, bulk-likelayers: (a) Te-terminated surface; (b) Br-terminated surface. z = 0 corresponds to the topmost atomic layer. ers of the crystal with respect to that in central, bulk-like layers. Such a potential change is negative at theTe-terminated surface and positive at the Cl(I) atom-terminated surface [29, 32], at that ∆ V bears a stepwisecharacter owing to clearly defined three-layered structureof bismuth tellurohalides. A similar behavior of ∆ V oc-curs on the surfaces of the ordered BiTeBr, as seen inFig. 3, where the change of the potential within the threeoutermost TLs on both surface terminations is shown.The negative ∆ V observed at the Te-terminated sur-face of the ordered BiTeBr leads to a downward shiftof energies of the electron states trapped in the step-wise surface potential (Fig. 4(a)). These states are pre-dominantly localized in the first three TLs. At the Br-terminated surface, an upward shift of energies of thetrapped states is provided by the positive ∆ V (Fig. 4(b)).The trapped states are offset in momentum, reflectinga large bulk spin-orbit splitting. They appear partiallyoverlapping the valence band continuum except the localenergy gap regions within bulk continuum states wherethe trapped states can be well resolved in ARPES at high binding energies. As a net result, for both terminationsthe changes of the electronic structure of BiTeBr underthe surface formation lead to emergence of the spin-splitsurface states in the bulk band gap (Fig. 5).At the Te-terminated surface (Fig. 5(a)), the spin-orbitsplit surface state localized in the topmost TL replicatesthe conduction band edge. The degeneracy point of thesurface spin-split state is 150 meV lower than the CBM.Within the energy gap region, the surface-state disper-sion demonstrates the free-electron-like parabolic char-acter. The spin splitting of the state is characterized by α R = 2 .
109 and 2.007 eV˚A in the ¯Γ − ¯K and ¯Γ − ¯Mdirections, respectively.The parabolic character of the surface state providescircular shape of the constant energy contours (CEC) forinner and outer branches of the spin-split surface state inthe bulk band gap region. As one can see in Fig. 6(a), inapproaching the bulk conduction band the CEC for theouter branch acquires the hexagonal deformation that isalready visible at 100 meV above the degeneracy point.The surface-state spin structure demonstrates counter-clockwise and clockwise in-plane helicity for the innerand outer branches, respectively, with a small S z spincomponent for both of them (Fig. 6(a)). Owing to sym-metry constrains, the expectation value of the S y and S z spin components vanishes along ¯Γ − ¯M , and they havemaximal values along ¯Γ − ¯K at any chosen energy. Inturn, S x is zero along ¯Γ − ¯K and reaches maximal valuesalong ¯Γ − ¯M direction. In Fig. 6(b), we show the absolutevalue of the cartesian spin components as functions of k || for the inner and outer branches of the spin-split surfacestate. As one can see, for a small k ¯K the | S z | componentis negligibly small, and, thus, the surface state is com-pletely in-plane spin polarized. This component startsrising at k ¯K > . − , i.e. at energy of 50 meV abovethe degeneracy point, which leads to a decrease of the in-plane spin components under approaching the bulk con-duction states. Thus, owing to (i) the parabolic energydispersion, (ii) outermost TL localization, and (iii) the in-plane helical spin structure within the band gap energyregion, the surface state on the Te-terminated surface ofBiTeBr(0001) can be described as the Rashba-split sur-face state with Rashba coupling parameter of ∼ − ¯K and ¯Γ − ¯M directions but they degeneratewith bulk states in the close vicinity of ¯Γ. Furthermore,the second outermost-TL localized state arises at ¯Γ in thevalley of the valence band. The appearance of the sec-ond pair of the spin-split states in the gap and the secondstate at ¯Γ is explained by the fact that the magnitude ofthe ∆ V is larger than that on the Te-terminated surface(see Fig. 3). Such a ∆ V provides a larger splitting off FIG. 4: Electronic structure of a BiTeBr(0001) slab: (a) Te-terminated surface; (b) Br-terminated surface. The red, pink, andorange circles denote weights of the states localized in the 1-st, 2-nd, and 3-rd TLs of the surface under consideration; lightgray circles mark the states localized on H-terminated side of the slab. The projected bulk band structure is shown in green. from the valence band edge.In general features, the band-gap-lying outermostTL-localized spin-orbit split surface state at the Br-terminated surface resembles those found at the halide-atom-terminated surface of BiTeCl and BiTeI [29, 32].This state demonstrates noticeable anisotropy of the en-ergy dispersion with respect to k || , which results in morecomplex shape of the CECs both above and below the de-generacy point (see Fig. 7). Such an anisotropic disper-sion is accompanied by an appreciably out-of-plane spinpolarization and entangled spin structure of the surfacestate, especially below the degeneracy point (Fig. 7).Formally, the spin-splitting of the Br-terminated sur-face state is characterized by k R = 0.079 and 0.077 ˚A − in ¯Γ − ¯K and ¯Γ − ¯M direction, respectively, and by E R equal to 130.2 meV (¯Γ − ¯K) and 125.6 meV (¯Γ − ¯M).These characteristics yield α R equal to 3.29 and 3.26 eV˚Afor ¯Γ − ¯K and ¯Γ − ¯M directions, respectively. However,this spin-split surface state can not be identified as the Rashba state owing to its dispersion and entangled spinstructure. CONCLUSIONS
Thus, we have investigated the atomic and electronicstructure of BiTeBr. The total energy calculations ofthe ordered and disordered phases of BiTeBr have shownthat the ordered structure is energetically preferable. Wehave found that the surfaces of the ordered BiTeBr holdsurface states which demonstrate a giant spin-orbit spinsplitting. These states emerge as a result of splitting offfrom the bulk conduction or valence band, owing to thepotential bending within the near-surface layers, like inother bismuth tellurohalides, BiTeCl and BiTeI, studiedearlier. The spin-split surface state at the Te-terminatedsurface, owing to its parabolic energy dispersion, out-ermost TL localization, and in-plane helical spin struc-
FIG. 5: Magnified view of electronic structure of Te-terminated (a) and Br-terminated (b) BiTeBr(0001) surface in the vicinityof ¯Γ [colors correspond to those marked in Fig. 4]. ture preserved within the whole band-gap energy region,can be described as a Rashba-split surface state with theRashba coupling parameter α R of ∼ k || anisotropy and entangled spin struc-ture can not be identified as the Rashba-split state andthus has less appeal than the spin split surface state atthe Te-terminated surface. [1] I. ˇZuti´c, J. Fabian, and S. Das Sarma, Rev. Mod.. Phys. , 323 (2004).[2] E.I. Rashba, Sov. Phys. Solid State , 1109 (1960); Y.A.Bychkov and E.I. Rashba, JETP Lett. , 78 (1984); J.Phys. C , 6039 (1984).[3] S. Datta and B. Das, Appl. Phys. Lett. , 665 (1990).[4] J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, Phys.Rev. Lett. , 1335 (1997).[5] D. Grundler, Phys. Rev. Lett. , 6074 (2000).[6] M. Studer, G. Salis, K. Ensslin, D.C. Driscoll, and A.C.Gossard, Phys. Rev. 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