Landau-level (LL) spectroscopy of epitaxial Sb2Te3 topological-insulator thin films (Jiang et al., Phys. Rev. Lett. 108, 016401 (2012)) established the linear Dirac dispersion of the surface states and a 4-quintuple-layer thickness limit for 3D topological-insulator behavior, and attributed LL peak broadening to intra-band electron-electron interaction (EEI) with a quasiparticle lifetime of ~0.2 ps and mean free path of ~80 nm. The same study explicitly left the microscopic scattering picture incomplete: step-edge-induced in-gap bound states and their role in limiting the mean free path were only inferred, possible magnetic-field enhancement of EEI and its effect on LL broadening was suggested but uncharacterized, and Sb-vacancy-induced spectral degradation was noted but not quantified. This problem asks for a mechanism-level, quantitative account of the channels that limit surface-state quasiparticle lifetimes and spectral quality in Sb2Te3 films: the origin and energy dependence of step-edge bound states, the field dependence of EEI-driven LL broadening, and the defect-species-resolved (Sb-on-Te antisites versus Sb vacancies) contribution to in-gap states and decoherence across growth conditions. Later work has partially addressed each thread in adjacent materials (Bi2Se3, Bi2Te3, (Bi,Sb)2Te3) and on cleaved bulk Sb2Te3, but no Sb2Te3-thin-film-specific resolution exists, and the dominant broadening mechanism remains contested between electron-electron-interaction and charged-impurity/disorder pictures.

Background

A three-dimensional topological insulator (TI) is a bulk insulator whose surfaces host an odd number of two-dimensional massless Dirac fermion bands produced by strong spin-orbit coupling. In Sb2Te3 the crystal is a stack of quintuple layers (QLs, five-atom Te-Sb-Te-Sb-Te slabs ~1 nm thick); the (111) surface is Te-terminated and carries a single Dirac cone (one linearly dispersing surface band) whose spin-momentum locking (helical spin texture) forbids elastic backscattering from nonmagnetic disorder. Molecular beam epitaxy (MBE, element-by-element vacuum deposition) growth of Sb2Te3 unavoidably produces high densities of intrinsic point defects, mainly Sb vacancies and Sb-on-Te antisite substitutions (both p-type dopants), which normally pin the Fermi level into or near the bulk valence band and obscure the surface states.

In scanning tunneling spectroscopy (STS, the spectroscopic mode of scanning tunneling microscopy, STM), a perpendicular magnetic field BB quantizes the Dirac surface states into Landau levels with energies En−ED=sgn(n) ℏvF2e∣n∣B/ℏE_n-E_D=\mathrm{sgn}(n)\,\hbar v_F\sqrt{2e|n|B/\hbar} relative to the Dirac-point energy EDE_D (the n=0n=0 level is pinned to EDE_D, a hallmark of massless Dirac fermions). The full width at half maximum Γ\Gamma of an LL peak is a measure of the inverse quasiparticle lifetime, τ≈ℏ/Γ\tau\approx\hbar/\Gamma, and the mean free path is vFτv_F\tau. The energy and field dependence of Γ\Gamma therefore diagnoses which microscopic channel limits quasiparticle coherence: electron-electron interaction (EEI) scattering rates grow with energy away from the Fermi level EFE_F but are suppressed near a Dirac point by phase-space restrictions; electron-phonon coupling turns on above characteristic phonon energies; static disorder broadens levels near EFE_F in a characteristic way; and charged-impurity scattering in Dirac systems has its own distinct power-law energy dependence.

Jiang et al. (Phys. Rev. Lett. 108, 016401 (2012)) used low-temperature STM/STS on MBE-grown Sb2Te3 films on graphene to observe LL quantization, extract a Fermi velocity vF≈4.3×105 m s−1v_F\approx4.3\times10^5\ \mathrm{m\,s^{-1}}, and demonstrate that 4 QL is the thickness limit for Sb2Te3 thin films to behave as a 3D topological insulator: in thinner films the Dirac surface states of the two opposite surfaces hybridize and open a gap. Their LL peak-width analysis showed minima near EFE_F and near the Dirac point and led them to attribute the broadening to intra-band EEI, ruling out the substitutional (Sb-on-Te) defects and electron-phonon coupling; a minimum width of ~4 meV gave τ≈0.2\tau\approx0.2 ps and a mean free path of ~80 nm. Three limitations were acknowledged explicitly. First, that mean free path is comparable to the terrace size of the films, so atomic step edges were suggested as the scattering source setting the upper limit, and step-edge-induced in-gap bound states were invoked on the basis of STM observations on Bi2Te3 (Alpichshev et al., Phys. Rev. B 84, 041104(R) (2011)); the paper proposed that Sb-on-Te antisites act as weak impurities that do not violate topological protection, in contrast to the strong impurity-induced in-gap resonances discussed for Bi2Se3. Second, the authors noted that EEI may be increased further in the presence of a magnetic field, without characterizing this effect on LL broadening or lifetime scaling. Third, a footnote records that Sb vacancies (which dominate in films grown at lower temperature) degrade the spectrum quality of 3 QL films, probably because Sb vacancies may have in-gap resonances, while antisite defects do not, but no systematic quantification across growth conditions was performed.

Problem Statement

Identify and quantify, at the microscopic level, the mechanisms that limit quasiparticle lifetimes and spectral quality of the topological surface states in Sb2Te3 thin films, as left open by the Landau-quantization study of Jiang et al. (Phys. Rev. Lett. 108, 016401 (2012)). The single common objective - a complete scattering/disorder/many-body account of the ~0.2 ps lifetime and ~80 nm mean free path observed in LL spectroscopy of these films - decomposes into three linked, jointly necessary channels, all for Sb2Te3 (thin films where the original measurements were made):

  1. Step-edge scattering channel: determine the microscopic origin and energy dependence of the in-gap bound states induced by the step edges one quintuple layer (~1 nm) high that bound the terraces of Sb2Te3 films, and assess whether and to what extent step-edge scattering (bound-state trapping plus reflection) sets the observed mean free path, which is comparable to the terrace size.

  2. Electron-electron interaction in magnetic field: characterize quantitatively the influence of EEI on Landau-level broadening and quasiparticle lifetime scaling in an applied magnetic field, in particular whether and how EEI is enhanced by the field, and disentangle this channel from disorder/charged-impurity and electron-phonon broadening - resolving the conflicting interpretations that later LL-linewidth studies on bulk Sb2Te3 have produced.

  3. Defect-species-resolved in-gap states and decoherence: determine how the two intrinsic defect species of Sb2Te3 (Sb-on-Te antisites versus Sb vacancies) contribute to in-gap resonant states and to decoherence of the surface quasiparticles, quantified systematically as a function of growth conditions (which select the dominant defect species), and whether the reported degradation of the Landau-level spectra in vacancy-dominated films follows from vacancy-induced in-gap states or from another channel.

The resolution sought is, for each channel, a mechanism assignment together with its energy and field dependence, and a quantitative account of how the channels combine to produce the measured LL widths, lifetimes, and mean free paths in Sb2Te3 films, specifically the observed ~4 meV minimum width, ~0.2 ps lifetime, and ~80 nm mean free path. The three channels are linked, and only a joint account gives the full scattering/disorder/many-body picture of that lifetime and mean free path.

References

  1. Yeping Jiang, Yilin Wang, Mu Chen, Zhi Li, Canli Song, Ke He, Lili Wang, Xi Chen, Xucun Ma, Qi-Kun Xue, 'Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3', Phys. Rev. Lett. 108, 016401 (2012). DOI: 10.1103/PhysRevLett.108.016401, https://doi.org/10.1103/PhysRevLett.108.016401 (arXiv:1111.1485, https://arxiv.org/abs/1111.1485)
  2. Yeping Jiang, Y. Y. Sun, Mu Chen, Yilin Wang, Zhi Li, Canli Song, Ke He, Lili Wang, Xi Chen, Qi-Kun Xue, Xucun Ma, S. B. Zhang, 'Fermi-Level Tuning of Epitaxial Sb2Te3 Thin Films on Graphene by Regulating Intrinsic Defects and Substrate Transfer Doping', Phys. Rev. Lett. 108, 066809 (2012). DOI: 10.1103/PhysRevLett.108.066809, https://doi.org/10.1103/PhysRevLett.108.066809 (arXiv:1111.0817, https://arxiv.org/abs/1111.0817)
  3. Zhanybek Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, A. Kapitulnik, 'STM imaging of a bound state along a step on the surface of the topological insulator Bi2Te3', Phys. Rev. B 84, 041104(R) (2011). DOI: 10.1103/PhysRevB.84.041104, https://doi.org/10.1103/PhysRevB.84.041104
  4. Rudro R. Biswas, Alexander V. Balatsky, 'Scattering from surface step edges in strong topological insulators', Phys. Rev. B 83, 075439 (2011). DOI: 10.1103/PhysRevB.83.075439, https://doi.org/10.1103/PhysRevB.83.075439
  5. Yishuai Xu, Guodong Jiang, Janet Chiu, Lin Miao, Erica Kotta, Yutan Zhang, Rudro R. Biswas, L. Andrew Wray, 'Connection topology of step edge state bands at the surface of a three dimensional topological insulator', New J. Phys. 20, 073014 (2018). DOI: 10.1088/1367-2630/aacef6, https://doi.org/10.1088/1367-2630/aacef6
  6. Naoya Fukui, Rei Hobara, Akari Takayama, Ryota Akiyama, Toru Hirahara, Shuji Hasegawa, 'Scattering of topological surface-state carriers at steps on surfaces', Phys. Rev. B 102, 115418 (2020). DOI: 10.1103/PhysRevB.102.115418, https://doi.org/10.1103/PhysRevB.102.115418
  7. C. Pauly, C. Saunus, M. Liebmann, M. Morgenstern, 'Spatially resolved Landau level spectroscopy of the topological Dirac cone of bulk-type Sb2Te3(0001): Potential fluctuations and quasiparticle lifetime', Phys. Rev. B 92, 085140 (2015). DOI: 10.1103/PhysRevB.92.085140, https://doi.org/10.1103/PhysRevB.92.085140 (arXiv:1506.03231, https://arxiv.org/abs/1506.03231)
  8. Oliver Storz, Paolo Sessi, Stefan Wilfert, Chris Dirker, Thomas Bathon, Konstantin Kokh, Oleg Tereshchenko, Matthias Bode, 'Landau Level Broadening in the Three-Dimensional Topological Insulator Sb2Te3', Phys. Status Solidi RRL 12, 1800112 (2018). DOI: 10.1002/pssr.201800112, https://doi.org/10.1002/pssr.201800112
  9. P. Sessi, O. Storz, T. Bathon, S. Wilfert, K. A. Kokh, O. E. Tereshchenko, G. Bihlmayer, M. Bode, 'Scattering properties of the three-dimensional topological insulator Sb2Te3: Coexistence of topologically trivial and nontrivial surface states with opposite spin-momentum helicity', Phys. Rev. B 93, 035110 (2016). DOI: 10.1103/PhysRevB.93.035110, https://doi.org/10.1103/PhysRevB.93.035110 (arXiv:1512.03895, https://arxiv.org/abs/1512.03895)
  10. Wenhan Zhang, Damien West, Seng Huat Lee, Yunsheng Qiu, Cui-Zu Chang, Jagadeesh S. Moodera, Yew San Hor, Shengbai Zhang, Weida Wu, 'Electronic fingerprints of Cr and V dopants in the topological insulator Sb2Te3', Phys. Rev. B 98, 115165 (2018). DOI: 10.1103/PhysRevB.98.115165, https://doi.org/10.1103/PhysRevB.98.115165
  11. Kane L. Scipioni, Zhenyu Wang, Yulia Maximenko, Ferhat Katmis, Charlie Steiner, Vidya Madhavan, 'Role of defects in the carrier-tunable topological-insulator (Bi_{1-x}Sb_x)_2Te_3 thin films', Phys. Rev. B 97, 125150 (2018). DOI: 10.1103/PhysRevB.97.125150, https://doi.org/10.1103/PhysRevB.97.125150 (arXiv:1709.09133, https://arxiv.org/abs/1709.09133)
  12. Yuxuan Jiang, Mahmoud M. Asmar, Xingyue Han, Mykhaylo Ozerov, Dmitry Smirnov, Maryam Salehi, Seongshik Oh, Zhigang Jiang, Wang-Kong Tse, Liang Wu, 'Electron-Hole Asymmetry of Surface States in Topological Insulator Sb2Te3 Thin Films Revealed by Magneto-Infrared Spectroscopy', Nano Lett. 20, 4588-4593 (2020). DOI: 10.1021/acs.nanolett.0c01447, https://doi.org/10.1021/acs.nanolett.0c01447 (arXiv:2004.01244, https://arxiv.org/abs/2004.01244)
  13. Dirk Backes, Danhong Huang, Rhodri Mansell, Martin Lanius, Jörn Kampmeier, David Ritchie, Gregor Mussler, Godfrey Gumbs, Detlev Grützmacher, Vijay Narayan, 'Thickness dependence of electron-electron interactions in topological p-n junctions', Phys. Rev. B 99, 125139 (2019). DOI: 10.1103/PhysRevB.99.125139, https://doi.org/10.1103/PhysRevB.99.125139