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Section
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Mathematics
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Title
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Two-dimensional difference Dirac operator in the strip
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Author(-s)
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Tinyukova T.S.a
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Affiliations
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Udmurt State Universitya
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Abstract
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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.
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Keywords
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discrete difference Dirac operator, resolution, spectrum
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UDC
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517.958, 530.145.6
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MSC
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81Q10, 81Q15
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DOI
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10.20537/vm150110
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Received
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1 February 2015
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Language
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Russian
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Citation
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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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References
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- Hasan M.Z., Kane C.L. Colloquium: topological insulators, Rev. Mod. Phys., 2010, vol. 82, pp. 3045-3067.
- Bardarson J.H., Moore J.E. Quantum interference and Aharonov-Bohm oscillations in topological insulators, Rep. Prog. Phys., 2012, vol. 76, 056501.
- Yokoyama T., Tanaka Y., Nagaosa N. Anomalous magnetoresistance of a two-dimensional ferromagnet / ferromagnet junction on the surface of a topological insulator, Phys. Rev. B., 2010, vol. 81, 121401 (R).
- Chuburin Y.P. Electron scattering on the surface of a topological insulator, Phys. A.: Math. Theor., 2014, vol. 47, 255203 (13 p).
- Morozova L.E., Chuburin Yu.P. On levels of the one-dimensional discrete Schrödinger operator with a decreasing small potential, Izv. Inst. Mat. Inform. Udmurt. Gos. Univ., 2004, no. 1 (29), pp. 85-94.
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Full text
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