Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Temperature-dependent electron and phonon dynamics in the ternary topological insulator (Bi1−xSbx)2Te3 at terahertz frequencies

Alexander Stroh1, Hassan A. Hafez1,*, Pascal Strathkötter1, Andrew D. Burnett3, John Kendrick3, Alessandra Di Gaspare4, Maik Gärner1, Judith Bünte1, Chiara Seidel1 et al.

Ahmet Yagmur4, Craig S. Knox2,4, Matthew Vaughan2, Nathan Fox2, Satoshi Sasaki4, Andreas Hütten1, Edmund Linfield2, Miriam S. Vitiello5, Joshua Freeman2, and Dmitry Turchinovich1,†

  • *Contact author: hafez@physik.uni-bielefeld.de
  • †Contact author: dmtu@physik.uni-bielefeld.de

Phys. Rev. B 112, 214303 – Published 1 December, 2025

DOI: https://doi.org/10.1103/y1qg-vjnz

Abstract

We investigate the temperature-dependent free electron conduction, terahertz phonon modes, and electron-phonon interactions, in the ternary topological insulator (Bi1−xSbx)2Te3. Terahertz time-domain spectroscopy and Raman spectroscopy on three n-type (Bi1−xSbx)2Te3 samples of various thicknesses were performed. Strong phonon activity and electron–phonon coupling were experimentally revealed and found to be sensitive to temperature changes and subtle structural variations between the samples. The experimental results, well described by Drude-Lorentz-Fano model, were compared to density functional theory calculations, yielding the phonon mode assignment. Further, an additional broadened background absorption was observed and attributed to the morphology of the conductive top surface of the samples.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (65)

  1. H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5, 438 (2009).
  2. D. Pesin and A. H. MacDonald, Spintronics and pseudospintronics in graphene and topological insulators, Nat. Mater. 11, 409 (2012).
  3. J. E. Moore, The birth of topological insulators, Nature (London) 464, 194 (2010).
  4. A. Anirban, 15 years of topological insulators, Nat. Rev. Phys. 5, 267 (2023).
  5. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature (London) 452, 970 (2008).
  6. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  7. P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh et al., Observation of Dirac plasmons in a topological insulator, Nat. Nanotechnol. 8, 556 (2013).
  8. S. Sim, N. Koirala, M. Brahlek, J. H. Sung, J. Park, S. Cha, M. H. Jo, S. Oh, and H. Choi, Tunable Fano quantum-interference dynamics using a topological phase transition in (Bi1−xInx)2Se3, Phys. Rev. B 91, 235438 (2015).
  9. R. Heid, I. Y. Sklyadneva, and E. V. Chulkov, Electron-phonon coupling in topological surface states: The role of polar optical modes, Sci. Rep. 7, 1095 (2017).
  10. B. W. Li, W. C. Jiang, G. Y. Chen, Y. Xiang, W. Xie, Y. M. Dai, X. Y. Zhu, H. Yang, and H. H. Wen, Anomalous phonon softening in the topological insulator Sn-doped Bi1.1Sb0.9Te2S, Sci. China Phys. Mech. Astron. 63, 117011 (2020).
  11. C. P. Schmid, L. Weigl, P. Grössing, V. Junk, C. Gorini, S. Schlauderer, S. Ito, M. Meierhofer, N. Hofmann, D. Afanasiev et al., Tunable non-integer high-harmonic generation in a topological insulator, Nature (London) 593, 385 (2021).
  12. Y. Bai, F. Fei, S. Wang, N. Li, X. Li, F. Song, R. Li, Z. Xu, and P. Liu, High-harmonic generation from topological surface states, Nat. Phys. 17, 311 (2021).
  13. S. Kovalev, K.-J. Tielrooij, J.-C. Deinert, I. Ilyakov, N. Awari, M. Chen, A. Ponomaryov, M. Bawatna, T. V. A. G. de Oliveira, L. M. Eng et al., Terahertz signatures of ultrafast Dirac fermion relaxation at the surface of topological insulators, npj Quantum Mater. 6, 84 (2021).
  14. F. Giorgianni, E. Chiadroni, A. Rovere, M. Cestelli-Guidi, A. Perucchi, M. Bellaveglia, M. Castellano, D. Di Giovenale, G. Di Pirro, M. Ferrario et al., Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator, Nat. Commun. 7, 11421 (2016).
  15. C.-K. Lee, J. H. Lee, B.-T. Zhang, and J.-L. He, Topological insulators and applications, in 2D Materials for Nanophotonics, edited by Y. M. Jhon (Elsevier, Amsterdam, 2021), pp. 81–138.
  16. X. Zhang, J. Wang and S. C. Zhang, Topological insulators for high-performance terahertz to infrared applications, Phys. Rev. B 82, 245107 (2010).
  17. M. Y. Toriyama and G. J. Snyder, Topological insulators for thermoelectrics: A perspective from beneath the surface, The Innovation 6, 100782 (2025).
  18. Q. Xia, Q. Xu, B. Xu, and L. Yi, Ab initio prediction of thermoelectric performance of monolayer BiSbTe3, J. Solid State Chem. 296, 121963 (2021).
  19. D. Baldomir and D. Faílde, On behind the physics of the thermoelectricity of topological insulators, Sci. Rep. 9, 6324 (2019).
  20. T. Yang, Y. Yang, X. Wang, G. Zhang, and Z. Cheng, Topological thermoelectrics: New opportunities and challenges, Mater. Today Chem. 30, 101488 (2023).
  21. D. Kong, Y. Chen, J. J. Cha, Q. Zhang, J. G. Analytis, K. Lai, Z. Liu, S. S. Hong, K. J. Koski, S.-K. Mo et al., Ambipolar field effect in the ternary topological insulator (BixSb1−x)2Te3 by composition tuning, Nat. Nanotechnol. 6, 705 (2011).
  22. J. Zhang, C.-Z. Chang, Z. Zhang, J. Wen, X. Feng, K. Li, M. Liu, K. He, L. Wang, X. Chen et al., Band structure engineering in (Bi1−xSbx)2Te3 ternary topological insulators, Nat. Commun. 2, 574 (2011).
  23. X. He, H. Li, L. Chen, and K. Wu, Substitution-induced spin-splitted surface states in topological insulator (Bi1−xSbx)2Te3, Sci. Rep. 5, 8830 (2015).
  24. L. Wu, M. Brahlek, R. V. Aguilar, A. V. Stier, C. M. Morris, Y. Lubashevsky, L. S. Bilbro, N. Bansal, S. Oh, and N. P. Armitage, A sudden collapse in the transport lifetime across the topological phase transition in (Bi1−xInx)2Se3, Nat. Phys. 9, 410 (2013).
  25. C. S. Knox, M. T. Vaughan, A. D. Burnett, M. Ali, S. Sasaki, E. H. Linfield, A. G. Davies, and J. R. Freeman, Effects of structural ordering on infrared active vibrations within Bi2(Te(1−x)Sex)3, Phys. Rev. B 106, 245203 (2022).
  26. V. S. Kamboj, A. Singh, T. Ferrus, H. E. Beere, L. B. Duffy, T. Hesjedal, C. H. W. Barnes, and D. A. Ritchie, Probing the topological surface state in Bi2Se3 thin films using temperature-dependent terahertz spectroscopy, ACS Photonics 4, 2711 (2017).
  27. B. C. Park, T. H. Kim, K. I. Sim, B. Kang, J. W. Kim, B. Cho, K. H. Jeong, M. H. Cho, and J. H. Kim, Terahertz single conductance quantum and topological phase transitions in topological insulator Bi2Se3 ultrathin films, Nat. Commun. 6, 6552 (2015).
  28. V. Chis, I. Y. Sklyadneva, K. A. Kokh, V. A. Volodin, O. E. Tereshchenko, and E. V. Chulkov, Vibrations in binary and ternary topological insulators: First-principles calculations and Raman spectroscopy measurements, Phys. Rev. B 86, 174304 (2012).
  29. Y. Zhao, X. Luo, J. Zhang, J. Wu, X. Bai, M. Wang, J. Jia, H. Peng, Z. Liu, S. Y. Quek et al., Interlayer vibrational modes in few-quintuple-layer Bi2Te3 and Bi2Se3 two-dimensional crystals: Raman spectroscopy and first-principles studies, Phys. Rev. B 90, 245428 (2014).
  30. R. R. Urkude and U. A. Palikundwar, Phonon dynamics of (Bi1−xSbx)2Te3 topological insulators by Raman spectroscopy, Physica B 655, 414754 (2023).
  31. R. E. Glover and M. Tinkham, Conductivity of superconducting films for photon energies between 0.3 and 40kTc, Phys. Rev. 108, 243 (1957).
  32. P. U. Jepsen, D. G. Cooke, and M. Koch, Terahertz spectroscopy and imaging—Modern techniques and applications, Laser Photon. Rev. 5, 124 (2011).
  33. L. S. Bilbro, R. V. Aguilar, G. Logvenov, O. Pelleg, I. Božović, and N. P. Armitage, Temporal correlations of superconductivity above the transition temperature in La2−xSrxCuO4 probed by terahertz spectroscopy, Nat. Phys. 7, 298 (2011).
  34. J. P. Heremans, R. J. Cava, and N. Samarth, Tetradymites as thermoelectrics and topological insulators, Nat. Rev. Mater. 2, 17049 (2017).
  35. R. P. S. M. Lobo, N. Bontemps, M. I. Bertoni, T. O. Mason, K. R. Poeppelmeier, A. J. Freeman, M. S. Park, and J. E. Medvedeva, Optical conductivity of mayenite: From insulator to metal, J. Phys. Chem. C 119, 8849 (2015).
  36. L. C. Davis and L. A. Feldkamp, Interaction of many discrete states with many continua, Phys. Rev. B 15, 2961 (1977).
  37. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, Fano resonances in nanoscale structures, Rev. Mod. Phys. 82, 2257 (2010).
  38. M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, Fano resonances in photonics, Nat. Photon. 11, 543 (2017).
  39. U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866 (1961).
  40. A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder et al., Commentary: The materials project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
  41. J. Kendrick and A. D. Burnett, PDielec: The calculation of infrared and terahertz absorption for powdered crystals, J. Comput. Chem. 37, 1491 (2016).
  42. W. Liu, L. Endicott, V. A. Stoica, H. Chi, R. Clarke, and C. Uher, High-quality ultra-flat BiSbTe3 films grown by MBE, J. Cryst. Growth 410, 23 (2015).
  43. Z. Wang, T. P. Ginley, S. V. Mambakkam, G. Chandan, Y. Zhang, C. Ni, and S. Law, Plasmon coupling in topological insulator multilayers, Phys. Rev. Mater. 4, 115202 (2020).
  44. T. Stauber, G. Gómez-Santos, and L. Brey, Plasmonics in topological insulators: Spin-charge separation, the influence of the inversion layer, and phonon-plasmon coupling, ACS Photonics 4, 2978 (2017).
  45. N. Dean, J. C. Petersen, D. Fausti, R. I. Tobey, S. Kaiser, L. V. Gasparov, H. Berger, and A. Cavalleri, Polaronic conductivity in the photoinduced phase of 1T-TaS2, Phys. Rev. Lett. 106, 016401 (2011).
  46. C. S. Tang, B. Xia, X. Zou, S. Chen, H. W. Ou, L. Wang, A. Rusydi, J. X. Zhu, and E. E. M. Chia, Terahertz conductivity of topological surface states in Bi1.5Sb0.5Te1.8Se1.2, Sci. Rep. 3, 3513 (2013).
  47. N. A. Kabir, Y. Yoon, J. R. Knab, J. Y. Chen, A. G. Markelz, J. L. Reno, Y. Sadofyev, S. Johnson, Y. H. Zhang, and J. P. Bird, Terahertz transmission characteristics of high-mobility GaAs and InAs two-dimensional-electron-gas systems, Appl. Phys. Lett. 89, 132109 (2006).
  48. S. Shimizu, R. Yoshimi, T. Hatano, K. S. Takahashi, A. Tsukazaki, M. Kawasaki, Y. Iwasa, and Y. Tokura, Gate control of surface transport in MBE-grown topological insulator (Bi1−xSbx)2Te3 thin films, Phys. Rev. B 86, 045319 (2012).
  49. N. Bansal, Y. S. Kim, E. Edrey, M. Brahlek, Y. Horibe, K. Iida, M. Tanimura, G.-H. Li, T. Feng, H.-D. Lee et al., Epitaxial growth of topological insulator Bi2Se3 film on Si(111) with atomically sharp interface, Thin. Solid. Films 520, 224 (2011).
  50. A. Fülöp, Y. Song, S. Charpentier, P. Shi, M. Ekström, L. Galletti, R. Arpaia, T. Bauch, F. Lombardi, and S. Wang, Phase transition of bismuth telluride thin films grown by MBE, Appl. Phys. Express 7, 045503 (2014).
  51. S. Schreyeck, K. Brunner, A. Kirchner, U. Bass, S. Grauer, C. Schumacher, C. Gould, G. Karczewski, J. Geurts, and L. W. Molenkamp, Kinetic limitation of chemical ordering in Bi2Te3−xSex layers grown by molecular beam epitaxy, J. Phys.: Condens. Matter 28, 145002 (2016).
  52. J. Hafner, Ab-initio simulations of materials using VASP: Density-functional theory and beyond, J. Comput. Chem. 29, 2044 (2008).
  53. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  54. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  55. S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
  56. A. D. Becke and E. R. Johnson, A density-functional model of the dispersion interaction, J. Chem. Phys. 123, 154101 (2005).
  57. H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
  58. J. D. Pack and H. J. Monkhorst, Special points for Brillouin-zone integrations”—A reply, Phys. Rev. B 16, 1748 (1977).
  59. A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys. Condens. Matter 35, 353001 (2023).
  60. A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Japan 92, 012001 (2023).
  61. J. Kendrick, https://Github.Com/JohnKendrick/PDielec, https://github.com/JohnKendrick/PDielec.
  62. J. Kendrick, A. D. Burnett and Authorea-Committer, JohnKendrick/PDielec: PDielec Version 8.2.0 Powder and Single Crystal Infrared Calculations, https://zenodo.org/records/14054801.
  63. M. Jeannin, https://Pygtm.Readthedocs.Io/En/Latest/, https://pygtm.readthedocs.io/en/latest/.
  64. N. C. Passler, M. Jeannin, and A. Paarmann, Layer-resolved absorption of light in arbitrarily anisotropic heterostructures, Phys. Rev. B 101, 165425 (2020).
  65. M. M. Bay, S. Vignolini, and K. Vynck, PyLlama: A stable and versatile Python toolkit for the electromagnetic modelling of multilayered anisotropic media, Comput. Phys. Commun. 273, 108256 (2022).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation