Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator
dc.contributor.author | Ortiz Martín, Laura | |
dc.contributor.author | Molina Fernández, Rafael Alejandro | |
dc.date.accessioned | 2023-06-18T06:54:52Z | |
dc.date.available | 2023-06-18T06:54:52Z | |
dc.date.issued | 2016-05-20 | |
dc.description | ©2016 American Physical Society. This work has been funded by Spanish Government projects: FIS2012-33152, FIS2012-34479, MAT2014-58241-P, FIS2015-63770-P and CAM research consortium QUITEMAD+ S2013/ICE-2801. AML acknowledges A. Fernandez Romero and financial support from the Carlsberg Foundation. | |
dc.description.abstract | We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model. | |
dc.description.department | Depto. de Física Teórica | |
dc.description.faculty | Fac. de Ciencias Físicas | |
dc.description.refereed | TRUE | |
dc.description.sponsorship | Comunidad de Madrid | |
dc.description.sponsorship | Ministerio de Economía y Competitividad (MINECO) | |
dc.description.sponsorship | Carlsberg Foundation | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/38621 | |
dc.identifier.doi | 10.1103/PhysRevB.93.205431 | |
dc.identifier.issn | 2469-9950 | |
dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevB.93.205431 | |
dc.identifier.relatedurl | http://journals.aps.org/ | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/24570 | |
dc.issue.number | 20 | |
dc.journal.title | Physical review B | |
dc.language.iso | spa | |
dc.page.final | 205431_19 | |
dc.page.initial | 205431_1 | |
dc.publisher | American Physical Society | |
dc.relation.projectID | QUITEMAD+ (S2013/ICE-2801) | |
dc.relation.projectID | FIS2012-33152 | |
dc.relation.projectID | FIS2012-34479 | |
dc.relation.projectID | MAT2014- 58241-P | |
dc.relation.projectID | FIS2015-63770-P | |
dc.rights.accessRights | open access | |
dc.subject.cdu | 53 | |
dc.subject.keyword | Hgte quantum-Wells | |
dc.subject.keyword | Neutrinos | |
dc.subject.keyword | Absence | |
dc.subject.keyword | Lattice | |
dc.subject.keyword | Proof | |
dc.subject.ucm | Física (Física) | |
dc.subject.unesco | 22 Física | |
dc.title | Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator | |
dc.type | journal article | |
dc.volume.number | 93 | |
dcterms.references | 1. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005). 2. C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005). 3. X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). 4. Y.Ando, J. Phys. Soc. Jpn. 82, 102001 (2013). 5. C. Xu and J. E. Moore, Phys. Rev. B 73, 045322 (2006). 6. M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Science 318, 766 (2007). 7. A. Roth, C. Brüne, H. Buhmann, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang,Science 325, 294 (2009). 8. C. Brüne, A. Roth, H. Buhmann, E. M. Hankiewicz, L. W. Molenkamp, J. Maciejko, X.-L. Qi, and S.-C. Zhang, Nat. Phys. 8, 485 (2012). 9. M. König, M. Baenninger, A. G. F. Garcia, N. Harjee, B. L. Pruitt, C. Ames, P. Leubner, C. Brüne, H. Buhmann, L. W. Molenkamp, and D. Goldhaber-Gordon, Phys. Rev. X 3, 021003 (2013). 10. B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006). 11. C. Liu, T. L. Hughes, X.-L. Qi, K. Wang, and S.-C. Zhang, Phys. Rev. Lett. 100, 236601 (2008). 12. I. Knez, R.-R. Du, and G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011). 13. K. Suzuki, Y. Harada, K. Onomitsu, and K. Muraki, Phys. Rev. B 87, 235311 (2013). 14. I. Knez, C. T. Rettner, S.-H. Yang, S. S. P. Parkin, L. Du, R.-R. Du, and G. Sullivan,Phys. Rev. Lett. 112, 026602 (2014). 15. L. Du, I. Knez, G. Sullivan, and R.-R. Du, Phys. Rev. Lett. 114, 096802 (2015). 16. F. Nichele, H. J. Suominen, M. Kjaergaard, C. M. Marcus, E. Sajadi, J. A. Folk, F. Qu, A. J. Beukman, F. K. de Vries, J. van Veen, S. Nadj-Perge, L. P. Kouwenhoven, B.-M. Nguyen, A. A. Kiselev, M. S. Wei Yi, M. J. Manfra, E. M. Spanton, and K. A. Moler, arXiv:1511.01728(2015). 17. G. M. Gusev, Z. D. Kvon, O. A. Shegai, N. N. Mikhailov, S. A. Dvoretsky, and J. C. Portal,Phys. Rev. B 84, 121302 (2011). 18. G. Grabecki, J. Wróbel, M. Czapkiewicz, L. Cywiński, S. Gierałtowska, E. Guziewicz, M. Zholudev, V. Gavrilenko, N. N. Mikhailov, S. A. Dvoretski, F. Teppe, W. Knap, and T. Dietl,Phys. Rev. B 88, 165309 (2013). 19. G. M. Gusev, Z. D. Kvon, E. B. Olshanetsky, A. D. Levin, Y. Krupko, J. C. Portal, N. N. Mikhailov, and S. A. Dvoretsky, Phys. Rev. B 89, 125305 (2014). 20. E. M. Spanton, K. C. Nowack, L. Du, G. Sullivan, R.-R. Du, and K. A. Moler, Phys. Rev. Lett. 113, 026804 (2014). 21. T. L. Schmidt, S. Rachel, F. von Oppen, and L. I. Glazman, Phys. Rev. Lett. 108, 156402 (2012). 22. A. Ström, H. Johannesson, and G. I. Japaridze, Phys. Rev. Lett. 104, 256804 (2010). 23. J. C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Phys. Rev. Lett. 108, 086602 (2012). 24. F. Crépin, J. C. Budich, F. Dolcini, P. Recher, and B. Trauzettel, Phys. Rev. B 86, 121106 (2012). 25. N. Lezmy, Y. Oreg, and M. Berkooz, Phys. Rev. B 85, 235304 (2012). 26. F. Geissler, F. Crépin, and B. Trauzettel, Phys. Rev. B 89, 235136 (2014). 27. N. Kainaris, I. V. Gornyi, S. T. Carr, and A. D. Mirlin, Phys. Rev. B 90, 075118 (2014). 28. J. I. Väyrynen, M. Goldstein, and L. I. Glazman, Phys. Rev. Lett. 110, 216402 (2013). 29. Y. Tanaka, A. Furusaki, and K. A. Matveev, Phys. Rev. Lett. 106, 236402 (2011). 30. A. M. Lunde and G. Platero, Phys. Rev. B 86, 035112 (2012). 31. E. Eriksson, A. Ström, G. Sharma, and H. Johannesson, Phys. Rev. B 86, 161103 (2012). 32. E. Eriksson, Phys. Rev. B 87, 235414 (2013). 33. B. Probst, P. Virtanen, and P. Recher, Phys. Rev. B 92, 045430 (2012). 34. A. M. Lunde and G. Platero, Phys. Rev. B 88, 115411 (2013). 35. D. G. Rothe, R. W. Reinthaler, C.-X. Liu, L. W. Molenkamp, S.-C. Zhang, and E. M. Hankiewicz, New J. Phys. 12, 065012 (2010). 36. P. Virtanen and P. Recher, Phys. Rev. B 85, 035310 (2012). 37. D. G. Rothe and E. M. Hankiewicz, Phys. Rev. B 89, 035418 (2014). 38. M. König, H. Buhmann, L. W. Molenkamp, T. L. Hughes, C.-X. Liu, X. L. Qi, and S. C. Zhang, J. Phys. Soc. Jpn. 77, 031007 (2008). 39. P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, Phys. Rev. B 86, 125323 (2012). 40. C. P. Orth, G. Strübi, and T. L. Schmidt, Phys. Rev. B 88, 165315 (2013). 41. C. P. Orth, R. P. Tiwari, T. Meng, and T. L. Schmidt, Phys. Rev. B 91, 081406 (2015). 42. A. Rod, T. L. Schmidt, and S. Rachel, Phys. Rev. B 91, 245112 (2015). 43. B. Zhou, H.-Z. Lu, R.-L. Chu, S.-Q. Shen, and Q. Niu, Phys. Rev. Lett. 101, 246807 (2008). 44. C. Liu and S.-C. Zhang, Models and Materials for Topological Insulators, edited by M. Franz and L. Molenkamp, Topological Insulators Vol. 7 (Springer, Vancouver, 2013). 45. S.-Q. Shen, Topological Insulators (Springer-Verlag, Hong Kong, 2011). 46. M. Wada, S. Murakami, F. Freimuth, and G. Bihlmayer, Phys. Rev. B 83, 121310 (2011). 47. B. A. Bernevig and with T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton University Press, New York, 2013). 48. P. Michetti, P. H. Penteado, J. C. Egues, and P. Recher, Semicond. Sci. Technol. 27, 124007 (2012). 49. V. Krueckl and K. Richter, Phys. Rev. Lett. 107, 086803 (2011). 50. W.-Y. Shan, H.-Z. Lu, and S.-Q. Shen, New J. Phys. 12, 043048 (2010). 51. Y. Takagaki, Phys. Rev. B 90, 165305 (2014). 52. A. Medhi and V. B. Shenoy, J. Phys.: Condens. Matter 24, 355001 (2012). 53. J. Linder, T. Yokoyama, and A. Sudbø, Phys. Rev. B 80, 205401 (2009). 54. C.-X. Liu, H. J. Zhang, B. Yan, X.-L. Qi, T. Frauenheim, X. Dai, Z. Fang, and S.-C. Zhang,Phys. Rev. B 81, 041307 (2010). 55. H.-Z. Lu, W.-Y. Shan, W. Yao, Q. Niu, and S.-Q. Shen, Phys. Rev. B 81, 115407 (2010). 56. J. J. Sakurai, Modern Quantum Mechanics (Addison Wesley, Geneva, 1993). 57. S. Murakami, S. Iso, Y. Avishai, M. Onoda, and N. Nagaosa, Phys. Rev. B 76, 205304 (2007). 58. M. Berry and R. J. Mondragon, Proc. R. Soc. London A 412, 53 (1987). 59. J. A. Fürst, J. G. Pedersen, C. Flindt, N. A. Mortensen, M. Brandbyge, T. G. Pedersen, and A.-P. Jauho, New J. Phys. 11, 095020 (2009). 60. P. Michetti and P. Recher, Phys. Rev. B 83, 125420 (2011). 61. Y. Baum, T. Posske, I. C. Fulga, B. Trauzettel, and A. Stern, Phys. Rev. Lett. 114, 136801 (2015). 62. K.-I. Imura, A. Yamakage, S. Mao, A. Hotta, and Y. Kuramoto, Phys. Rev. B 82, 085118 (2010). 63. H. Nielsen and M. Ninomiya, Nucl. Phys. B 185, 20 (1981). 64. H. Nielsen and M. Ninomiya, Nucl. Phys. B 193, 173 (1981). 65. R. Winkler, Spin-orbit Coupling Effects in Two-Dimensional Electron and Hole Systems, Springer Tracts in Modern Physics (Springer, Aarhus, 2003). | |
dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1