MATHEMATICS

Majorana states in the non-Hermitian infinite Bogolyubov–de Gennes model with non-reciprocal transitions

T. S. Tinyukova^a, Yu. P. Chuburin<sup>b

a</sup> Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
^b Udmurt Federal Research Center of the Ural Branch of the Russian Academy of Sciences, ul. T. Baramzinoi, 34, Izhevsk, 426067, Russia

Abstract: The lattice non-Hermitian Bogolyubov–de Gennes model of superconductivity is considered, based on the periodic Kitaev model, with local potentials of two types. One of them generates non-reciprocal electron–electron and hole–hole transitions, while the other generates a non-reciprocal electron–hole transition. Conditions for the existence and analytical formulas for eigenfunctions with zero eigenvalue describing Majorana states are found.

Keywords: Bogolyubov-de Gennes model, non-Hermitianity, eigenfunctions

UDC: 517.958, 530.145.6, 517.984

MSC: 81Q10, 81Q15, 47A10, 47A40

Received: 07.07.2025
Accepted: 18.10.2025

DOI: 10.35634/2226-3594-2025-66-08

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