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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, Volume 25, Issue 1, Pages 93–100
(Mi vuu468)
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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.
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
Linking options:
https://www.mathnet.ru/eng/vuu468 https://www.mathnet.ru/eng/vuu/v25/i1/p93
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Abstract page: | 294 | Full-text PDF : | 152 | References: | 46 |
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