Photoemission Spectroscopy of Magnetic and Non-magnetic Impurities on the Surface of the Bi 2 Se 3 Topological Insulator
PPhotoemission Spectroscopy of Magnetic and Non-magnetic Impurities on the Surfaceof the Bi Se Topological Insulator
T. Valla, ∗ Z.-H. Pan, D. Gardner, Y.S. Lee, and S. Chu Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY 11973 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (Dated: October 29, 2018)Dirac-like surface states on surfaces of topological insulators have a chiral spin structure that sup-presses back-scattering and protects the coherence of these states in the presence of non-magneticscatterers. In contrast, magnetic scatterers should open the back-scattering channel via the spin-flipprocesses and degrade the state’s coherence. We present angle-resolved photoemission spectroscopystudies of the electronic structure and the scattering rates upon adsorption of various magneticand non-magnetic impurities on the surface of Bi Se , a model topological insulator. We reveal aremarkable insensitivity of the topological surface state to both non-magnetic and magnetic impu-rities in the low impurity concentration regime. Scattering channels open up with the emergence ofhexagonal warping in the high-doping regime, irrespective of the impurity’s magnetic moment. PACS numbers: 74.25.Kc, 71.18.+y, 74.10.+v
Topological insulators (TIs) belong to a new class ofinsulators in which the bulk gap is inverted due to thestrong spin-orbit coupling. On the boundaries or in-terfaces of these materials with ordinary (”trivial”) in-sulators, gapless states inevitably occur, topologicallyprotected by the time reversal symmetry [1–3]. Three-dimensional topological insulators have surface stateswith an odd number of massless Dirac cones in whichthe spin of an electron is locked perpendicular to its mo-mentum in a chiral spin-structure where electrons withopposite momenta have opposite spins [4–10]. A directconsequence of this spin-momentum locking is that abackscattering, which would require a spin-flip process,is not allowed if a time- reversal-invariant perturbation,such as non-magnetic disorder, is present [4]. This makestopological insulators potentially very promising materi-als that could serve as a platform for spintronics and forquantum computing applications, where spin-coherenceis crucial. In contrast, a time-reversal symmetry break-ing perturbation, such as introduction of magnetic impu-rities on the surface, is expected to open a back-scatteringchannel and induce a gap at the Dirac point of the topo-logical surface state (TSS) [11–17].Even though it might be expected that these funda-mental predictions would be checked very quickly, theexperiments that would directly probe the sensitivity ofthe TSS and differentiate between the two types of dis-order are still lacking. Scanning tunneling microscopy(STM) experiments have shown that backscattering isindeed strongly suppressed or completely absent, despitestrong atomic scale disorder [18–20]. In angle resolvedphotoemission spectroscopy (ARPES), there has beenvery little quantitative work on the scattering rates. Onestudy [21] has indicated that the major decay channel forthe TSS is scattering into the bulk states, either elasti-cally, on defects, or inelastically, via the electron-electron interaction. More recent studies have also shown thatthe adsorption of various non-magnetic atomic/molecularspecies on the surface of a topological insulator induceselectronic doping and partial filling of additional spin-orbit split states [22, 23]. It has been also suggestedthat magnetic impurities, both in the bulk and on thesurface, open a small gap at the Dirac point [16, 17].However, the most fundamental question - how the mag-netic moment of an impurity affects the scattering - hasremained unanswered. Even for non-magnetic perturba-tions, it would be highly desirable to know how the TSSbehaves as the concentration of impurities increases andhow it is affected by the presence of other states thatbecome partially occupied by electron doping. Wouldthe presence of such states, that come in spin-orbit splitpairs, therefore allowing inter-band scattering, both withand without spin-flip, degrade the TSS’ coherence? Or,would the intra-band scattering dominate? We note thatnone of these questions have been addressed in experi-ments and that there has been no systematic studies ofthe scattering rates on any kind of impurities.Here, we present quantitative experimental studies ofscattering rates on on the surface of Bi Se , a model TI.We directly compare the effects of non- magnetic andmagnetic impurities on the TSS and, quite unexpectedly,we find that there is essentially no difference betweenthese two types of scatterers. Both the scattering andthe impurity induced development of the surface elec-tronic structure seem remarkably insensitive to the typeof disorder. Instead, we find that the scattering rates aresensitive to the Fermi surface shape, which can be tunedby the doping, irrespective of the impurity’s magneticmoment. We also find no evidence for an opening of agap at the Dirac point of the TSS.The single crystal samples were synthesized by mix-ing stoichiometric amounts of bismuth and selenium with a r X i v : . [ c ond - m a t . s t r- e l ] M a r FIG. 1: Surface doping of Bi Se . a) to d) ARPES spectra from Bi Se at various stages of Rb deposition, showing the Fermisurface (upper panels) and the (E, k ) dispersion of photoemission intensity along the momentum line slightly off the ΓM line inthe surface Brillouin zone (lower panels). a) pristine surface, b) intermediate doping and c) maximal doping, taken at hν = 21 . hν = 18 . trace amounts of arsenic in evacuated quartz tubes [24].The ARPES experiments were carried out at the U13UBbeamline of the National Synchrotron Light Source withthe photons in the range between 15.5 and 22 eV. Theelectron analyzer was a Scienta SES-2002 with the com-bined energy resolution around 8 meV and the angularresolution of ∼ . ◦ . Samples were cleaved in-situ inthe UHV chamber with the base pressure of 3 × − Pa.Ni was deposited using an e-beam evaporator, Cu andGd were evaporated from a resistively heated tungstenbasket, while alkalies were deposited from commercial(SAES) getter sources with the samples kept at ∼
15 Kduring the deposition and ARPES measurements.Figure 1 shows the development of surface electronicstructure upon deposition of rubidium on the Bi Se sur-face. The rapidly dispersing conical band in the pristinesample represents the TSS with the Dirac point around0.32 eV below the Fermi level. At binding energy higherthan 0.4 eV the TSS overlaps with the bulk valence band(BVB) and near the Fermi level, the bulk conductingband (BCB) is visible inside the surface state cone, in-dicating the electron doping of Bi Se by Se vacancies.The TSS has an almost perfectly circular Fermi surface.Upon Rb deposition, TSS is further doped with electrons,evident from the down-shift of the Dirac point and thegrowing Fermi surface that acquires a pronounced hexag-onal warping. However, this is not the only effect of dop-ing: new states are also being formed and progressivelyfilled with electrons donated by adsorbed Rb. In panelsc) and d) we show the stage of Rb deposition at whichthe maximal charge transfer into the surface electronicstructure of Bi Se is reached. At this stage, in additionto the original TSS, two pairs of new states are visible atlower binding energies. Each pair consists of two spin-orbit split states, displaced in momentum in a Rashba- type manner, intersecting at new Dirac points at the zonecenter. These states also have surface character as theydo not disperse with k z . At the highest doping levels,the outermost state becomes almost degenerate with theTSS, forming the Fermi surface nearly equal in shape andsize. Its inner counterpart is significantly smaller, retain-ing the perfectly circular Fermi surface, even at the high-est doping. We also observe new valence states below theDirac point of the TSS. Although their dispersion nearthe zone center resembles the dispersion of the BVB, thelack of k z dispersion indicates their surface character.Fig. 1e) summarizes the changes in some of the mea-sured quantities with Rb doping. The surface dopinglevel was determined by measuring the Fermi surface areaof the TSS and of the lower Rashba-split doublet: A T (TSS), A O (outer Rashba state) and A I (inner Rashbastate). The upper Rashba doublet was not taken intoaccount. The total charge (per surface unit cell) is then q = ( A T + A O + A I ) /A BZ , where A BZ = 2 .
662 ˚A − repre-sents the Brillouin zone area. At maximal doping, nearly0.105 e − per surface unit cell is transferred from Rb intothe three states shown here. If the second pair of states(better resolved in Fig. 2c) is counted, then the totalcharge transfer is ∼ e − . The surface charge density n = q/A UC , where A UC = 44 .
487 ˚A is the area of theunit cell in real space, could be tuned from ∼ × cm − (clean sample) to ∼ × cm − (maximal dop-ing). As a Rb atom can donate at most one electron, themeasured charge transfer implies that the average Rb-Rbdistance could be shorter than 3 unit cells. Scattering onRb would then lead to the very short mean free pathfor surface electrons ( ∼ (cid:96) = 1 / ∆ k in the range of 100˚A, where ∆ k is the momentum spread of the Fermi sur- FIG. 2: Development of the surface electronic structure withCesium (a), Gadolinium (b) and Rubidium (c) adsorption atthe surface of Bi Se . The spectra were recorded along theΓM line in the surface Brillouin zone and at hν = 18 . hν = 21 . face, measured from the momentum distribution curves(MDCs) [25]. Insensitivity to impurity scattering mightbe expected for the TSS, but only in the absence of otherstates that could open the inter-band scattering channels.Thus, the retained coherence of all the detected states issomewhat surprising.In Fig. 2, we compare the effects of different adsor-bates on the surface electronic structure of Bi Se - inparticular we compare the non- magnetic impurities, Rband Cs, with Gd whose atoms have large magnetic mo-ments, ∼ µ B . We have also studied adsorbed Ni andCu (not shown). Surprisingly, there is no visible differ-ence in the spectra for different adsorbates, if taken at thesame photon energy. In the recent study where iron wasdeposited on Bi Se , the electronic structure also looksvery similar [17]. Relative intensities of the states thatform the Fermi surface depend on photon energy, reflect-ing the variation of ARPES matrix elements. Thus, thehigher pair of Rashba-split states, hardly visible in Csand Gd covered surface is clearly resolved in Rb dopedsystem, measured at different photon energy. However,none of these states disperse with k z , reflecting their sur-face character. We also note that the maximal dopinglevel achievable with different adsorbates increases fromNi to Gd to Cu to Rb to Cs. FIG. 3: ImΣ( ω ) of the topological surface state upon adsorp-tion of Rubidium (a) and Gadolinium (b) for several differentdoping levels, as indicated. c) and d) show ImΣ( ω ) of thelower Rashba-split doublet for Rb and Gd doped surfaces,respectively, near the maximum doping. The most important observation from the spectra inFig. 2 is that, contrary to the expectations, the magneticstate of the adsorbate does not seem to play a significantrole in the scattering. At similar stages of doping withdifferent adsorbates, the TSS seems similarly coherent.The same is true for the Rashba- split states. Further, itappears that all the adsorbates have a similar effect onthe spectral region around the Dirac point of TSS, withno clear gap formation.In Fig. 3 we show the imaginary part of the quasi-particle self-energy, | ImΣ( ω ) | = Γ( ω ) /
2, where Γ( ω ) rep-resents the scattering rate, as a function of binding en-ergy for TSS for several different concentrations of Rband Gd atoms on the surface of Bi Se . Scattering ratesare determined from Γ( ω ) = 2 | ImΣ( ω ) | = ∆ k ( ω ) v ( ω ),where ∆ k ( ω ) is the measured full width at half maxi-mum of the Lorentzian-fitted peak in MDC, and v ( ω ) isthe group velocity of the state at energy ω . The TSS re-mains very coherent until the concentration of adsorbedatoms reaches the level at which the Fermi surface be-comes heavily hexagonally warped, regardless of whetherthe adsorbates are magnetic or non-magnetic. For simi-lar doping levels, the scattering rates are essentially thesame for Rb and Gd covered surfaces. Pristine surfacesand surfaces with relatively low concentration of impu-rities, show very low ImΣ at the Fermi level, indicatinglong coherence lengths of TSS, (cid:96) >
150 ˚A. Even at thedoping levels ∼ .
05 e − per surface unit cell, where theaverage distance between the impurities is shorter than ∼ ∝ ω , indicating that the inelas-tic electron- electron scattering has a Fermi-liquid-likeform. For high impurity concentrations, ∼ . − persurface unit cell, ImΣ reaches the value of ∼
40 meV at
FIG. 4: a) Development of the surface electronic structure with Cs doping. Middle panel shows shift of the states at k x = 0 . k x = 0 .
03 ˚A( k x = 0) point. the Fermi level, corresponding to the mean free path of ∼
70 ˚A, and is nearly energy independent. Due to thepartial overlap with the significantly more intense outerRashba state, we could not reliably determine the widthof the TSS at low energies. We also show the ImΣ forthe two states that form the lower Rashba-split doublet.There is a significant difference between the states form-ing the doublet: the outer state is significantly broaderthan the inner one and is similar in width to the TSSat this concentration level. This is again true for bothmagnetic and non-magnetic impurities.In Fig. 4 we illustrate the effects of Cs and Gd de-position on the spectral region near the Dirac point ofTSS. We show the spectral intensity at the point slightlydisplaced from the k x = 0 (middle panels) and exactlyat the k x = 0 point (right panels), as a function of Csand Gd deposition time. Contrary to the expectations,both metals have similar effects: with the deposition ofthese metals, it seems as if the lower and the upper partsof the Dirac cone penetrate each other. Thus, at smallbut finite k x , the two branches merge and possibly in-tersect after ∼ k x = 0, once the gap opens. Our resultssuggest that neither of the adsorbates opens a clear gapat the Dirac point of the TSS. We also see no evidence ofa gap at the second Dirac point, where the states form-ing the lower Rashba-split doublet intersect (Fig. 2).This suggests that the Kramer’s points, i.e. the pointswhere the spins are degenerated in the unperturbed sys-tem, are more robust to magnetic perturbations than ex-pected. One possible reason for this insensitivity couldbe a strongly localized magnetic moment ( f orbitals) inadsorbed Gd, resulting in a very small scattering cross-section. However, similar results for adsorbed nickel andiron [17] with the more delocalized moments, would argue against this explanation.Our experiments show that the quasi-particle scatter-ing on the surface of a TI is not affected by magneticmoments of impurity atoms. This might imply that thescattering rates are dominated by the small momentumtransfer events and not by back-scattering. Then, theexistence of multiple Fermi surfaces, allowing both theintra-band and inter-band scattering, and the observa-tion that the inner Rashba-split Fermi surface is alwayssharper than its outer counterpart and the TSS mightsuggest that the former one has the opposite spin helic-ity than the latter two. However, recent calculations [17]suggest that the spin helicities of these three states alter-nate (L-R-L). If this is the case, our results would implythat the inter-band scattering is strongly suppressed. In-deed, we do not see any anomalies in the scattering ratesat the thresholds for the inter-band channels. Therefore,we could conclude that the observed broadening with ad-sorption of impurities reflects the increase in intra- bandscattering as the size and the warping of the Fermi surfacegrows with doping [9, 11, 13, 26, 27]. We note that theseeffects will likely play determining role in a performanceof any electronic device based on a topological insulator,because any environmental doping will inevitably affectthe surface state mobility, µ S = e(cid:96) tr / (¯ hk F ), in transportexperiments. Even though the transport mean free path, (cid:96) tr , might be significantly longer than (cid:96) , especially whenback-scattering is suppressed, our results indicate thatmobilities will be reduced by the doping, implying thatthe full potential of TIs could only be realized in a con-trolled, preferably ultra-high vacuum environment, or byan inert capping of the surface.In conclusion, we have observed that magnetic mo-ment of an impurity does not play a dominant role inthe scattering of the TSS. However, with the increasingdoping, the state becomes warped, and the scatteringeventually increases - irrespective of impurity’s magneticmoment. Therefore, the TSS does not remain protectedindefinitely, even when doped with non-magnetic impu-rities. 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