Abstract
We study spectra of surface states in 2D topological insulators based on HgTe/(Hg,Cd)Te quantum wells and 3D Bi2Se3-type compounds by constructing a class of feasible time-reversal invariant boundary conditions (BCs) for an effective kp-Hamiltonian and a tight-binding model of the topological insulators. The BCs contain some phenomenological parameters which implicitly depend on both bulk Hamiltonian parameters and crystal potential behavior near the crystal surface. Space symmetry reduces the number of the boundary parameters to four real parameters in the 2D case and three in the 3D case. We found that the boundary parameters may strongly affect not only an energy spectrum but even the very existence of these states inside the bulk gap near the Brillouin zone center. Nevertheless, we reveal in frames of the tight-binding model that when surface states do not exist in the bulk gap in the Brillouin zone center they cross the gap in other points of the Brillouin zone in agreement with the bulk-boundary correspondence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Hasan and C. Kane, Rev. Mod. Phys. 82, 3045 (2010).
X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).
Topological Insulators, Ed. by M. Franz and L. Molenkamp (Elsevier, Amsterdam, 2013).
L. Isaev, Y. H. Moon, and G. Ortiz, Phys. Rev. B 84, 075444 (2011).
G. M. Graf and M. Porta, Commun. Math. Phys. 324, 851 (2013).
S. S. Pershoguba and V. M. Yakovenko, Phys. Rev. B 86, 075304 (2012).
J. Linder, T. Yokoyama, and A. Sudb_, Phys. Rev. B 80, 205401 (2009).
B. Zhou, H.-Z. Lu, R.-L. Chu, S.-Q. Shen, and Q. Niu, Phys. Rev. Lett. 101, 246807 (2008).
C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Zh. Fang, and Sh.-Ch. Zhang, Phys. Rev. B 82, 045122 (2010).
A. Medhi and V. B. Shenoy, J. Phys.: Condens. Matter 24, 355001 (2012).
V. N. Men’shov, V. V. Tugushev, and E. V. Chulkov, JETP Lett. 98, 603 (2013).
V. N. Men’shov, V. V. Tugushev, T. V. Menshchikova, S. V. Eremeev, P. M. Echenique, and E. V. Chulkov, J. Phys.: Condens. Matter 26, p. 485003 (2014); arXiv:1406.7191.
E. L. Ivchenko, Optical Spectroscopy of Semiconductor Nanostructures (Alpha Science, Harrow, UK, 2005).
Zh. A. Devizorova, A. V. Shchepetilnikov, Yu. A. Nefyodov, V. A. Volkov, and I. V. Kukushkin, JETP Lett. 100, 102 (2014).
B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Science 314, 1757 (2006).
O. E. Raichev, Phys. Rev. B 85, 045310 (2012).
V. A. Volkov and T. N. Pinsker, Sov. Phys. Solid State 23, 1022 (1981).
B. A. Volkov, B. G. Idlis, and M. Sh. Usmanov, Phys. Usp. 38, 761 (1995).
L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007).
S. G. Davison and M. Steslicka, Basic Theory of Surface States (Clarendon, Oxford, 1992).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Enaldiev, V.V., Zagorodnev, I.V. & Volkov, V.A. Boundary conditions and surface state spectra in topological insulators. Jetp Lett. 101, 89–96 (2015). https://doi.org/10.1134/S0021364015020071
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021364015020071