Abstract:
Using the Bogoliubov–de Gennes Hamiltonian, we analytically study two models with superconducting order, the p-wave model with an impurity potential and the s-wave nanowire model with superconductivity induced by the proximity effect with an impurity potential in a Zeeman field with a spin–orbit interaction. Using the Dyson equation, we study conditions for the emergence of Andreev bound states with energies close to the boundary of the superconducting gap and the possibility for these states to pass into Majorana-like bound states. We prove that in the topological phase (in the p-wave case also in the trivial phase) for both models, the Andreev bound states with energy close to the boundary of the superconducting gap can exist, but although their emergence in the p-wave model is due to the appearance of a (nonmagnetic) impurity, they appear in the s-wave model only as a result of a local perturbation of the Zeeman field. For both models, the transition of the Andreev bound states into the Majorana states (and back) is impossible in the topological phase, which is explained by the topological protection of the Majorana-like bound states in the topological phase.
The research of Yu. P. Chuburin was supported by
the Urals Branch of the Russian Academy of Sciences
(Program No. AAAA-A16-116021010082-8).
The research of T. S. Tinyukina was supported by the Ministry of Education and Science of the Russian Federation under state
mission No. 075-00232-20-01, Project No. 0827-2020-0010 “Development of
theory and methods of control and stabilization of dynamical systems.”
Citation:
Yu. P. Chuburin, T. S. Tinyukova, “Mutual transition of Andreev and Majorana bound states in a superconducting gap”, TMF, 205:3 (2020), 484–501; Theoret. and Math. Phys., 205:3 (2020), 1666–1681
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\by Yu.~P.~Chuburin, T.~S.~Tinyukova
\paper Mutual transition of Andreev and Majorana bound states in a~superconducting gap
\jour TMF
\yr 2020
\vol 205
\issue 3
\pages 484--501
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\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 205
\issue 3
\pages 1666--1681
\crossref{https://doi.org/10.1134/S0040577920120089}
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https://www.mathnet.ru/eng/tmf9951
https://doi.org/10.4213/tmf9951
https://www.mathnet.ru/eng/tmf/v205/i3/p484
This publication is cited in the following 2 articles:
Yu. P. Chuburin, T. S. Tinyukova, “Interaction between subbands in a quasi-one-dimensional superconductor”, Theoret. and Math. Phys., 210:3 (2022), 398–410
Yu. P. Chuburin, T. S. Tinyukova, “Behaviour of Andreev states for topological phase transition”, Theoret. and Math. Phys., 208:1 (2021), 977–992
Citation in format AMSBIB
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