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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 1, Pages 93–100 (Mi vuu468)  

This article is cited in 2 scientific papers (total in 2 papers)

MATHEMATICS

Two-dimensional difference Dirac operator in the strip

T. S. Tinyukova

Department of Mathematical Analysis, Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia

Abstract: In the last decade, a new class of materials – topological insulators – is extensively studied in the physics literature. Topological insulators have remarkable physical properties, in particular, near-zero resistance, and are expected to be applied in microelectronics. Unlike conventional metals and semiconductors, an electron in topological insulators is described not by the Schrodinger operator (Hamiltonian), but by the massless Dirac operator. Such operators in quasi-one-dimensional structures (for example, strips with different boundary conditions) are very interesting from a mathematical point of view, but they are not well studied by mathematicians yet. This article discusses the Dirac Hamiltonian of a topological insulator of somewhat more general form, namely in the presence of a ferromagnetic layer. The spectrum of such an operator is described; its Green's function (the kernel of the resolvent) and (generalized) eigenfunctions are established.

Keywords: discrete difference Dirac operator, resolution, spectrum.

Full text: PDF file (185 kB)
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UDC: 517.958+530.145.6
MSC: 81Q10, 81Q15
Received: 01.02.2015

Citation: T. S. Tinyukova, “Two-dimensional difference Dirac operator in the strip”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:1 (2015), 93–100

Citation in format AMSBIB
\Bibitem{Tin15}
\by T.~S.~Tinyukova
\paper Two-dimensional difference Dirac operator in the strip
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 1
\pages 93--100
\mathnet{http://mi.mathnet.ru/vuu468}
\elib{http://elibrary.ru/item.asp?id=23142056}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. S. Tinyukova, “Kvaziurovni dvumernogo raznostnogo operatora Diraka v polose”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 26:4 (2016), 535–542  mathnet  crossref  mathscinet  elib
    2. T. S. Tinyukova, “O rasseyanii i kvaziurovnyakh v modeli SSH”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:2 (2017), 257–266  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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