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Pis'ma v Zh. Èksper. Teoret. Fiz., 2015, Volume 102, Issue 3, Pages 216–224 (Mi jetpl4701)  

This article is cited in 5 scientific papers (total in 5 papers)


Simple counterexample for the $\mathcal{Z}_2$ classification of topological insulators based on the bulk-boundary correspondence

S. N. Molotkovabc, M. I. Ryzhkinb

a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia
b Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432, Russia
c Academy of Cryptography of the Russian Federation, Moscow, 121552, Russia

Abstract: The so-called $\mathcal{Z}_2$ classification of topological insulators has been previously proposed on the basis of the bulk-boundary correspondence. This classification is commonly accepted and involves the following statements [L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007)]: (i) nontrivial $\mathcal{Z}_2$ invariants imply the existence of gapless surface states, (ii) the $\mathcal{Z}_2$ invariants can be deduced from the topological structure of the Bloch wave functions of the bulk crystal in the Brillouin zone. In this work, a simple counterexample has been given for the $\mathcal{Z}_2$ classification. It has been shown that both topologically stable and topologically unstable surface states can exist on surfaces, at the same bulk, at the same space symmetry of a semi-infinite crystal, and, correspondingly, at a trivial value of the $\mathcal{Z}_2$ invariant (at the trivial class of equivalence of the bulk Hamiltonian) for the $3\mathrm{D}\to 2\mathrm{D}$ system. Furthermore, topologically stable surface states can exist at both trivial (Bi(111) surface) and nontrivial (Sb(111) surface) values of the bulk $\mathcal{Z}_2$ invariant. In view of these facts, the statement that the $\mathcal{Z}_2$ classification based on the bulk-boundary correspondence is responsible for the appearance and topological stability of surface states is doubtful.


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English version:
Journal of Experimental and Theoretical Physics Letters, 2015, 102:3, 189–197

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Received: 20.04.2015
Revised: 23.06.2015

Citation: S. N. Molotkov, M. I. Ryzhkin, “Simple counterexample for the $\mathcal{Z}_2$ classification of topological insulators based on the bulk-boundary correspondence”, Pis'ma v Zh. Èksper. Teoret. Fiz., 102:3 (2015), 216–224; JETP Letters, 102:3 (2015), 189–197

Citation in format AMSBIB
\by S.~N.~Molotkov, M.~I.~Ryzhkin
\paper Simple counterexample for the $\mathcal{Z}_2$ classification of topological insulators based on the bulk-boundary correspondence
\jour Pis'ma v Zh. \`Eksper. Teoret. Fiz.
\yr 2015
\vol 102
\issue 3
\pages 216--224
\jour JETP Letters
\yr 2015
\vol 102
\issue 3
\pages 189--197

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    This publication is cited in the following articles:
    1. JETP Letters, 102:11 (2015), 754–759  mathnet  crossref  crossref  isi  elib
    2. Galeeva A.V. Egorova S.G. Chernichkin V.I. Tamm M.E. Yashina L.V. Rumyantsev V.V. Morozov S.V. Plank H. Danilov S.N. Ryabova L.I. Khokhlov D.R., Semicond. Sci. Technol., 31:9 (2016), 095010  crossref  isi  elib  scopus
    3. Samokhin K.V. Truong B.P., Phys. Rev. B, 95:13 (2017), 134514  crossref  isi  scopus
    4. S. I. Bozhko, A. S. Ksenz, A. M. Ionov, S. V. Chekmazov, E. A. Levchenko, JETP Letters, 107:12 (2018), 780–784  mathnet  crossref  crossref  isi  elib  elib
    5. Chekmazov V S. Smirnov A.A. Ksenz A.S. Bozhko I S. Ionov A.M. Protasov S.G. Kapustin A.A. Vilkov O.Yu. Levchenko E.A., Mater. Lett., 240 (2019), 69–72  crossref  isi  scopus
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