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Russia Izhevsk
Section Mathematics
Title Two-dimensional difference Dirac operator in the strip
Author(-s) Tinyukova T.S.a
Affiliations Udmurt State Universitya
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
UDC 517.958, 530.145.6
MSC 81Q10, 81Q15
DOI 10.20537/vm150110
Received 1 February 2015
Language Russian
Citation Tinyukova T.S. Two-dimensional difference Dirac operator in the strip, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 1, pp. 93-100.
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