Geodesic
Scattering and quasilevels in the SSH model
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 2, pp. 257-266 Cet article a éte moissonné depuis la source Math-Net.Ru

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Topological insulator is a special type of material that represents an insulator in the interior (“in bulk”) and conducts electricity on the surface. The simplest topological insulator is a finite chain of atoms in polyacetylene. In the last decade topological insulators are actively studied in the physics literature. A great interest to topological insulators (and also to topologically similar superconducting systems) is due to the presence of a link between “volume” and “boundary”. In this article, we have studied the discrete model SSH (Su–Schrieffer–Heeger) for polyacetylene. This model describes an electron in a one-dimensional chain of atoms with two alternating amplitudes of the transition to a neighboring atom. We have found the spectrum and resolution of this operator. The quasilevels (eigenvalues and resonances) in the case of a small potential have been investigated. In addition, we obtained a solution of the Lippmann–Schwinger equation and asymptotic formulas for the probability of transmission and reflection in case of small perturbation.
Keywords: resolution, spectrum, eigenvalue, resonance, Lippmann–Schwinger equation, probability of reflection. 
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     author = {T. S. Tinyukova},
     title = {Scattering and quasilevels in the {SSH} model},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {257--266},
     year = {2017},
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     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2017_27_2_a8/}
}
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T. S. Tinyukova. Scattering and quasilevels in the SSH model. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 27 (2017) no. 2, pp. 257-266. http://geodesic.mathdoc.fr/item/VUU_2017_27_2_a8/

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