Measurement of an Exceptionally Weak Electron-Phonon Coupling on the Surface of the Topological Insulator Bi 2 Se 3 Using Angle-Resolved Photoemission Spectroscopy
Z.-H. Pan, A. V. Fedorov, D. Gardner, Y. S. Lee, S. Chu, T. Valla
MMeasurement of an Exceptionally Weak Electron-Phonon Coupling on the Surface ofthe Topological Insulator Bi Se Using Angle-Resolved Photoemission Spectroscopy
Z.-H. Pan, A. V. Fedorov, D. Gardner, Y.S. Lee, S. Chu, and T. Valla ∗ Condensed Matter Physics and Materials Science Department, Brookhaven National Lab, Upton, NY 11973 Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 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)Gapless surface states on topological insulators are protected from elastic scattering on non-magnetic impurities which makes them promising candidates for low-power electronic applications.However, for wide-spread applications, these states should have to remain coherent at ambient tem-peratures. Here, we studied temperature dependence of the electronic structure and the scatteringrates on the surface of a model topological insulator, Bi Se , by high resolution angle-resolved pho-toemission spectroscopy. We found an extremely weak broadening of the topological surface statewith temperature and no anomalies in the state’s dispersion, indicating exceptionally weak electron-phonon coupling. Our results demonstrate that the topological surface state is protected not onlyfrom elastic scattering on impurities, but also from scattering on low-energy phonons, suggestingthat topological insulators could serve as a basis for room temperature electronic devices. PACS numbers: 74.25.Kc, 71.18.+y, 74.10.+v
Three-dimensional topological insulators (TIs) haveDirac-like surface states in which the spin of the electronis locked perpendicular to its momentum in a chiral spin-structure where electrons with opposite momenta haveopposite spins [1–8]. A direct consequence of the chiralspin-structure is that a backscattering, which would re-quire a spin-flip process, is not allowed if a time- reversal-invariant perturbation, such as non-magnetic disorder, ispresent [1], making these surface states promising can-didates for spintronics and quantum computing applica-tions, where the spin-coherence is crucial. [9–15]. Recentscanning tunneling microscopy (STM) experiments [16–20] have shown that backscattering is indeed stronglysuppressed or completely absent, despite strong atomicscale disorder. Our own angle-resolved photoemissionspectroscopy (ARPES) studies have indicated that thestate is remarkably insensitive to both non-magnetic andmagnetic impurities in the low doping regime, where theFermi surface (FS) is nearly circular. The scattering isfound to increases as the FS becomes hexagonally warpedwith increased doping, irrespective of the impurity’s mag-netic moment [21].While the elastic scattering imposes the ultimate limiton the charge transport, the inelastic scattering processesdictate material’s transport properties at finite temper-atures. In particular, interactions of electrons with lat-tice modes is responsible for increasing resistivity withtemperature in metals. The same interaction may alsolead to a ground states with broken symmetries, suchas superconductivity or charge-density-wave state. Sofar, inelastic scattering processes at surfaces of TIs havebeen scarcely studied, with only one theoretical studyon the coupling of the topological surface states (TSS)to phonons [22]. As the lattice modes in general do not represent a time-reversal symmetry breaking perturba-tion, it might be expected that the TSS should not cou-ple to the q ≈ k F phonons. Therefore, scattering onphonons should resemble scattering on non-magnetic im-purities, where the rates are shown to be sensitive to theFermi surface size and shape [21]. On the other hand,the proximity of bulk states, which in some cases couldbe strongly coupled to phonons (occurrence of supercon-ductivity upon Cu-doping in Bi Se and under pressurein Bi Te [23–25]), could also influence the TSS by allow-ing the inter-band electron-phonon scattering. As theseprocesses will play a crucial role in determining perfor-mances of any real devices based on TIs, their betterunderstanding is an imperative.In this Letter, we present the high resolution ARPESstudies of the scattering rates on the surface of a TI,Bi Se . We observe a very weak temperature broaden-ing of the TSS and no anomaly in the state’s dispersiondue its coupling to phonons. Our results show that theelectron-phonon coupling is suppressed in a similar wayas the elastic scattering, suggesting that TIs could serveas a basis for room temperature applications.The experiments were carried out on a Scienta SES-100 electron spectrometer at the beamline 12.0.1 of theAdvanced Light Source (ALS) and on a Scienta 2002analyzer at the beamline U13UB of the National Syn-chrotron Light Source (NSLS). The spectra were recordedat the photon energy of 50 eV and 18.7 eV, with thecombined instrumental energy resolution of ∼
12 meVand ∼ ± . ◦ in both instru-ments. The single crystals of Bi Se were synthesized bymixing stoichiometric amounts of bismuth and seleniumwith trace amounts of arsenic in evacuated quartz tubes a r X i v : . [ c ond - m a t . s t r- e l ] J a n [26]. Samples were cleaved at low temperature (15-20K) under ultra-high vacuum (UHV) conditions (2 × − Pa). The temperature was measured using a silicon sen-sor mounted near the sample.
FIG. 1: Temperature effects on the ARPES spectra fromBi Se . (a) Fermi surface of Bi Se at 18 K. (b) ARPESintensity along the ΓK line in the surface Brillouin zone at18K and (c) at 255 K. Photoemission intensity at the Fermilevel (d) and at E = −
270 meV (e) along the ΓK momentumline as a function of temperature. (f) Photoemission inten-sity at the Γ point as a function of temperature. Sample washeated from 18 K to 255 K and then cooled back to 18 K.
Fig. 1 illustrates the effects of raising temperature onthe electronic structure of Bi Se measured in ARPESaround the center of the surface Brillouin zone. Therapidly dispersing conical state in Fig. 1b) and c) repre-sents the TSS that forms a circular Fermi surface shownin Fig. 1a. Its filling varies with temperature as evidentfrom the shift of the Dirac point from ≈ .
27 eV belowthe Fermi level at 18 K to ≈ .
23 eV at 255 K. Thistemperature induced shift and the corresponding changein the Fermi surface area are fully reversible upon tem-perature cycling as can be seen in panels d) to f). Wenote that at the pressure of 2 × − Pa, TSS is verystable if kept at constant temperature, without notice-able changes in the spectra several hours after cleaving.Therefore, the effects shown in Fig. 1 reflect the intrinsictemperature induced changes in the quasi-particle dy-namics rather than some spurious effects caused by ad-sorption/desorption of residual gases. We note that simi- lar shifts in binding energy of the state with temperaturewere observed in Shockley-type surface states on noblemetals. These shifts could be explained in the simplephase accumulation model where the phase change onthe crystal side of the potential well, that determines theenergy of the surface state, is affected by slight changesin the bulk band gap as temperature is varied [27]. In thecase of Bi Se , the bulk valence band (BVB) is expectedto have the dominating effect on the energy of the Diracpoint. The upward shift of the Dirac point, would indi-cate that the BVB also shifts up and that the bulk bandgap in Bi Se decreases with increasing temperature.To quantify the changes in the spectral width of TSS,we have analyzed the photoemission spectra at differ-ent temperatures using the standard method where themomentum distribution curves (MDCs) are fitted withLorentzian peaks [28, 29]. The width of the Lorentzianpeak, ∆ k ( ω ), is related to the quasiparticle scatteringrate Γ( ω ) = 2 | ImΣ( ω ) | = ∆ k ( ω ) v ( ω ), where v ( ω ) isthe bare group velocity and ImΣ( ω ) is the imaginary partof the complex self-energy. Fig. 2 shows several MDCscorresponding to the spectrum from Fig. 1b) and sum-marizes the results of the analysis. The spectral regionabove the Dirac point is very clean: it consists of twoLorentzian-shaped peaks with essentially no backgroundintensity, the fact that makes the fitting procedure veryaccurate. The bulk conduction band is absent as at thechosen photon energy of 50 eV, that corresponds approx-imately to the Z point in the bulk Brillouin zone, it laysabove the Fermi level. In contrast, the spectral region be-low the Dirac point is always affected by the BVB. Thefitting results for the region above the Dirac point areshown in panel b). ImΣ displays a weaker energy depen-dence than ∆ k , reflecting an increasing group velocity asthe state approaches the Fermi level. However, the mostimportant observation here is that ImΣ near the Fermilevel shows very little change between 18 K and 255 K.Temperature broadening of a quasi-particle peak usuallyreflects an increase in the scattering on phonons and itsnear absence here points to a very weak coupling of TSSto phonons in Bi Se . The electron-phonon coupling con-stant, λ , can be determined from the temperature slope ofImΣ(0) because at higher temperatures, approximately k B T > Ω /
3, the electron-phonon self energy | I m Σ( ω, T ) | = π (cid:90) ∞ dνα F ( ν )[2 n ( ν )+ f ( ν + ω )+ f ( ν − ω )](1)is approximately linear in temperature, ImΣ(0 , T ) ≈ λπk B T . Here α F ( ω ) is the Eliashberg coupling func-tion, f ( ω ) and n ( ω ) are the Fermi and Bose-Einsteinfunctions, Ω is energy of the highest involved phononand k B is Boltzmann’s constant [30]. In panel c), weplot ImΣ averaged over -20 meV < ω < FIG. 2: Temperature broadening of TSS on Bi Se . (a) Momentum distribution curves (MDCs) corresponding to the spectrumshown in Fig. 1(b), spaced by 50 meV, with the top curve representing the Fermi level. (b) Momentum width ∆ k (bottom)and ImΣ (top) of the Lorentzian-shaped MDC peaks at several different temperatures. Standard deviations from the fittingare within 5% of the obtained value (not shown) (c) Temperature dependence of ImΣ(0) for three different samples (bottom), E D (middle) and doping level of TSS for sample A (top). Solid lines are the linear fits of ImΣ(0). value. Samples A and C were measured at 50 eV, whilesample B was measured at 18.7 eV photon energy. Differ-ences in the TSS’s width are partially due to the differentmomentum resolution at these two photon energies andpartially due to the natural variation in the surface ”qual-ity”. However, in all three samples ImΣ increases withtemperature at a similar rate. The increase starts at lowtemperatures, indicating the involvement of low energyphonons. The linear fits give λ = 0 . ± .
007 for sampleA and 0 . ± .
009 for sample B. This represents one ofthe weakest coupling constants ever reported in any ma-terial, weaker than the theoretical value from ref. [22],but in agreement with the apparent absence of tempera-ture broadening of TSS in recent experiments on severaltopological materials [31]. In contrast, the occurrence ofsuperconductivity upon Cu-doping in Bi Se and underpressure in Bi Te [23–25] suggests much stronger cou-pling in the bulk of these materials. The estimate for thebulk coupling constant can be made by using the knownvalues for Debye temperatures [32] and superconductingtransition temperatures ( T c ) [23–25] in McMillan’s for-mula for T c [33]: λ = 0 .
62 (0.6) is obtained for Cu x Bi Se (Bi Te ), almost an order of magnitude stronger than ourresult for the surface state.Another indication of the exceptionally weak electron-phonon coupling at the surface is the apparent absenceof a mass enhancement in the dispersion of TSS near theFermi level. In Fig. 3 we show the low energy regionof the ARPES spectrum from Fig. 1b). A hallmark ofthe quasiparticle coupling to phonons in the form of asudden change in the slope or a ”kink” in dispersion in- side the phonon-energy range [29] is conspicuously miss-ing. The MDC derived dispersion in Fig. 3 is essentiallya straight line with no anomalies in the vicinity of theFermi level, in agreement with previous studies [31]. Wenote that the temperature dependence from Fig. 2c) re-quires the involvement of low energy modes which, inaddition to the very weak coupling, makes the observa-tion of an anomaly in dispersion extremely difficult andit would require a much better experimental resolution.We also note that the finite experimental resolution prob- FIG. 3: Zoom in the low-energy region of the ARPES spec-trum from Bi Se from Fig. 1b). Dispersion of TSS (solidline) is obtained from positions of Lorentzian-fitted peaks inMDCs. ably already affects the extracted values of ImΣ at lowtemperatures and that λ obtained from temperature de-pendence might be slightly underestimated.Our results should have very important consequenceson the macroscopic properties of the Bi Se surface, inparticular on the surface state’s contribution to trans-port - a crucial aspect for any (spin) electronic devicebased on TSS. The surface contribution to transport hasproven elusive due to the overwhelming bulk componentto conductivity and/or low surface state mobility in theenvironment of a typical transport measurement [34–38].The determining factor for transport is the surface state FIG. 4: Quasiparticle mean-free path (cid:96) (bottom) and µ qp (top) as functions of temperature, determined from theARPES spectra for samples A and B from Fig. 2c). Grayregions represent the limits of these quantities in doped sur-faces [21]. mobility, which can be expressed as µ S = e(cid:96) tr / (¯ hk F ) forthe Dirac-like carriers. Here, (cid:96) tr , represents the trans-port mean free path. In ARPES experiments, k F and thequasiparticle mean-free path (cid:96) = (∆ k ) − can be directlymeasured. In Fig. 4, we plot the quasiparticle mean freepath and the quantity µ qp = e(cid:96)/ (¯ hk F ), which may serveas a lower bound for surface state mobility, as functionsof temperature for samples A and B. We note that (cid:96) tr might be significantly longer than (cid:96) , because currents ingeneral are not sensitive to the small angle scatteringevents that may dominate (cid:96) . This discrepancy might beespecially enhanced in systems in which the backscatter-ing is suppressed, as in the case of TSSs, and we mightexpect significantly higher mobilities than µ qp shown inFig. 4. Therefore, the unperturbed and strongly coherentTSSs, as those measured here, have a strong potential toserve as a basis for room temperature spintronic devices.However, the environmental exposure will inevitably af-fect the coherence of the topological state and degrade its mobility, in a similar way as it was demonstrated inref. [21]. We note that recent transport experimentshave detected quantum oscillations related to the TSS,yielding surface mobilities of around 10 cm V − s − onthe surface of Bi Te [37], still low compared to thosemeasured in suspended graphene or in the best semicon-ductors [39, 40]. We suggest that controlled (ultra-highvacuum) environment and/or an inert capping of the sur-face would further improve the mobilities of TSS and thatsuch measures might be necessary for optimal functioningof TI-based devices.In summary, we have observed a weak electron-phononcoupling on the surface of Bi Se demonstrating that TSSis well protected from scattering on low-energy phonons.This keeps the possibility that TSSs could serve as a basisfor room-temperature devices open.The work at Brookhaven is supported by the US De-partment of Energy (DOE) under Contract No. DE-AC02- 98CH10886. The work at MIT is supported bythe DOE under Grant No. DE-FG02-04ER46134. ALSis operated by the US DOE under Contract No. DE-AC03-76SF00098. ∗ Electronic address: [email protected][1] L. Fu, C. L. Kane, and E. J. Mele, Phys. Rev. Lett. ,106803 (2007).[2] H. J. Noh, H. Koh, S. J. Oh, J. H. Park, H. D. Kim, J. D.Rameau, T. Valla, T. E. Kidd, P. D. Johnson, Y. Hu,et al., EPL , 57006 (2008).[3] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J.Cava, and M. Z. Hasan, Nature , 970 (2008).[4] H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, andS. C. Zhang, Nature Physics , 438 (2009).[5] D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier,J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong,et al., Nature , 1101 (2009).[6] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin,A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, et al., NaturePhys. , 398 (2009).[7] Y. L. Chen, J. G. Analytis, J. H. Chu, Z. K. Liu, S. K.Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang,et al., Science , 178 (2009).[8] Z.-H. Pan, E. Vescovo, A. V. Fedorov, D. Gardner, Y. S.Lee, S. Chu, G. D. Gu, and T. Valla, Phys. Rev. Lett. , 257004 (2011).[9] R. R. Biswas and A. V. Balatsky, Phys. Rev. B ,233405 (2010).[10] L. Fu, Phys. Rev. Lett. , 266801 (2009).[11] H.-M. Guo and M. Franz, Phys. Rev. B , 041102(2010).[12] Q. Liu, C.-X. Liu, C. Xu, X.-L. Qi, and S.-C. Zhang,Phys. Rev. Lett. , 156603 (2009).[13] X. Zhou, C. Fang, W.-F. Tsai, and J. Hu, Phys. Rev. B , 245317 (2009).[14] Y. L. Chen, J. H. Chu, J. G. Analytis, Z. K. Liu,K. Igarashi, H. H. Kuo, X. L. Qi, S. K. Mo, R. G. Moore,D. H. Lu, et al., Science , 659 (2010). [15] L. A. Wray, S. Y. Xu, Y. Xia, D. Hsieh, A. V. Fedorov,Y. S. Hor, R. J. Cava, A. Bansil, H. Lin, and M. Z. Hasan,Nature Phys. , 32 (2010).[16] P. Roushan, J. Seo, C. V. Parker, Y. S. Hor, D. Hsieh,D. Qian, A. Richardella, M. Z. Hasan, R. J. Cava, andA. Yazdani, Nature , 1106 (2009).[17] T. Zhang, P. Cheng, X. Chen, J. F. Jia, X. C. Ma, K. He,L. L. Wang, H. J. Zhang, X. Dai, Z. Fang, et al., Phys.Rev. Lett. , 266803 (2009).[18] Z. Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher,Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik,Phys. Rev. Lett. , 016401 (2010).[19] J. Seo, P. Roushan, H. Beidenkopf, Y. S. Hor, R. J. Cava,and A. Yazdani, Nature , 343 (2010).[20] T. Hanaguri, K. Igarashi, M. Kawamura, H. Takagi, andT. Sasagawa, Phys. Rev. B , 081305 (2010).[21] T. Valla, Z. Pan, D. Gardner, Y. S. Lee, and S. Chu,Phys. Rev. Lett. , 117601 (2012).[22] S. Giraud and R. Egger, Phys. Rev. B , 245322 (2011).[23] Y. S. Hor, A. J. Williams, J. G. Checkelsky, P. Roushan,J. Seo, Q. Xu, H. W. Zandbergen, A. Yazdani, N. P. Ong,and R. J. Cava, Phys. Rev. Lett. , 057001 (2010).[24] J. L. Zhang, S. J. Zhang, H. M. Weng, W. Zhang, L. X.Yang, Q. Q. Liu, S. M. Feng, X. C. Wang, R. C. Yu, L. Z.Cao, et al., PNAS , 24 (2011).[25] M. Kriener, K. Segawa, Z. Ren, S. Sasaki, and Y. Ando,Physical Review Letters , 127004 (2011), ISSN 0031-9007.[26] H. Steinberg, D. R. Gardner, S. L. Young, and P. Jarillo-Herrero, Nano Letters , 5032 (2010).[27] R. Paniago, R. Matzdorf, G. Meister, and A. Goldmann,Surface Science , 113 (1995).[28] T. Valla, A. V. Fedorov, P. D. Johnson, B. O. Wells, S. L. Hulbert, Q. Li, G. D. Gu, and N. Koshizuka, Science ,2110 (1999).[29] T. Valla, A. V. Fedorov, P. D. Johnson, and S. L. Hulbert,Phys. Rev. Lett. , 2085 (1999).[30] G. Grimvall, The Electron-Phonon Interaction in Metals (North- Holland, New York, 1981).[31] S. R. Park, W. S. Jung, G. R. Han, Y. K. Kim, C. Kim,D. J. Song, Y. Y. Koh, S. Kimura, K. D. Lee, N. Hur,et al., New Journal of Physics , 013008 (2011).[32] G. Shoemake, J. Rayne, and R. Ure, Physical Review , 1046 (1969).[33] W. McMillan, Physical Review , 331 (1968), ISSN0031-899X.[34] N. P. Butch, K. Kirshenbaum, P. Syers, A. B. Sushkov,G. S. Jenkins, H. D. Drew, and J. Paglione, Phys. Rev.B , 241301 (2010).[35] J. G. Analytis, J. H. Chu, Y. L. Chen, F. Corredor, R. D.McDonald, Z. X. Shen, and I. R. Fisher, Phys. Rev. B , 205407 (2010).[36] J. G. Analytis, R. D. McDonald, S. C. Riggs, J. H. Chu,G. S. Boebinger, and I. R. Fisher, Nature Phys. , 960(2010).[37] D. X. Qu, Y. S. Hor, J. Xiong, R. J. Cava, and N. P.Ong, Science , 821 (2010).[38] K. Eto, Z. Ren, A. A. Taskin, K. Segawa, and Y. Ando,Phys. Rev. B , 195309 (2010).[39] J. J. Harris, C. T. Foxon, K. W. J. Barnham, D. E.Lacklison, J. Hewett, and C. White, Journal of AppliedPhysics , 1219 (1987).[40] K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg,J. Hone, P. Kim, and H. Stormer, Solid State Communi-cations146