Mots-clés : Majorana state.
@article{TMF_2021_208_2_a9,
author = {A. G. Sergeev},
title = {On mathematical problems in the~theory of~topological insulators},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {342--354},
year = {2021},
volume = {208},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_208_2_a9/}
}
A. G. Sergeev. On mathematical problems in the theory of topological insulators. Teoretičeskaâ i matematičeskaâ fizika, Tome 208 (2021) no. 2, pp. 342-354. http://geodesic.mathdoc.fr/item/TMF_2021_208_2_a9/
[1] D. J. Thouless, M. Kohmoto, M. P. Nightingale, M. den Nijs, “Quantized Hall conductance in a two-dimensional periodic potential”, Phys. Rev. Lett., 49:6 (1982), 405–408 | DOI
[2] A. G. Sergeev, “Primeneniya nekommutativnoi geometrii v analize i matematicheskoi fizike”, Tr. MMO, 81:2 (2020), 1–59 | DOI
[3] A. Kitaev, “Periodic table for topological insulators and superconductors”, AIP Conf. Proc., 1134:1 (2009), 22–30 | DOI | Zbl
[4] C. L. Kane, E. J. Mele, “$\mathbb Z_2$ topological order and the quantum spin Hall effect”, Phys. Rev. Lett., 95:14 (2005), 146802, 4 pp. | DOI
[5] N. Ashkroft, N. Mermin, Fizika tverdogo tela, Mir, M., 1979 | Zbl
[6] E. M. Lifshits, L. P. Pitaevskii, Teoreticheskaya fizika, v. 9, Statisticheskaya fizika. Chast 2. Teoriya kondensirovannogo sostoyaniya, Fizmatlit, M., 2004 | MR
[7] R. Fox, “Homotopy groups and torus homotopy groups”, Ann. Math. (2), 49:2 (1948), 471–510 | DOI | MR
[8] J. E. Avron, R. Seiler, B. Simon, “Homotopy and quantization in condensed matter physics”, Phys. Rev. Lett., 51:1 (1983), 51–53 | DOI
[9] H. B. Lawson, Jr., M.-L. Michelsohn, Spin Geometry, Princeton Mathematical Series, 38, Princeton Univ. Press, Princeton, NJ, 1989 | MR
[10] S. Q. Shen, Topological Insulators: Dirac Operators in Condensed Matters, Springer, Berlin, 2013
[11] M. F. Atiyah, I. M. Singer, “Index theory for skew-adjoint Fredholm operators”, Inst. Haut. Étud. Sci. Publ. Math., 37 (1969), 5–26 | DOI | MR | Zbl
[12] M. F. Atiyah, I. M. Singer, “The index of elliptic operators. V”, Ann. Math., 93 (1971), 139–149 | DOI | MR
[13] R. M. Kaufmann, Dan Li, B. Wehefritz-Kaufmann, Topological insulators and K-theory, arXiv: 1510.08001
[14] F. A. Berezin, M. A. Shubin, The Schrödinger Equation, Mathematics and Its Applications (Soviet Series), 66, Springer, Dordrecht, 1991 | DOI | MR
[15] M. V. Berry, “Quantum phase factors accompanying adiabatic changes”, Proc. Roy. Soc. London Ser. A, 392:1802 (1984), 45–57 | DOI | MR
[16] F. Wilchek, A. Shapers, Geometric Phases in Physics, Advanced Series in Mathematical Physics, 5, World Sci., Singapore, 1989 | DOI | MR
[17] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1989 | DOI | MR | MR | Zbl | Zbl