Behavior of Andreev states for topological phase transition

Theoretical and Mathematical Physics - We consider three one-dimensional superconducting structures: 1) the one with $$p$$ -wave superconductivity; 2) the main experimental model of a nanowire with...     

Majorana States Near an Impurity in the Kitaev Infinite and Semi-Infinite Model

Theoretical and Mathematical Physics - For an infinite Kitaev chain with an impurity described by a deltalike potential, we analytically prove that two overlapping Majorana bound states in a...     

Mutual transition of Andreev and Majorana bound states in a superconducting gap

Theoretical and Mathematical Physics - Using the Bogoliubov–de Gennes Hamiltonian, we analytically study two models with superconducting order, the p-wave model with an impurity potential and...     

Electron scattering by a crystal layer

We consider the one-particle discrete Schrödinger operator H with a periodic potential perturbed by a function ?W that is periodic in two variables and exponentially decreasing in the third variable. Here, ? is a small parameter. We study the scattering problem for H near the point of extremum with respect to the third quasimomentum coordinate for a certain eigenvalue of the Schrödinger operator with a periodic potential in the cell, in other words, for the small perpendicular component of the angle of particle incidence on the potential barrier ?W. We obtain simple formulas for the transmission and reflection probabilities.     

Interaction between subbands in a quasi-one-dimensional superconductor

Theoretical and Mathematical Physics - In the framework of the Bogoliubov–de Gennes equation, we study the spinless $$p$$ -wave superconductor in an infinite strip in the presence of some...     

Andreev states in a quasi-one-dimensional superconductor on the surface of a topological insulator

Theoretical and Mathematical Physics - We study bound states in an s-wave superconducting strip on the surface of a topological superconductor with the perpendicular Zeeman field. We prove...     

The Role of Majorana-Like Bound States in the Andreev Reflection and the Josephson Effect in the Case of a Topological Insulator

Theoretical and Mathematical Physics - We analytically investigate Andreev bound states with a near-zero energy in a one-dimensional “normal metal-superconductor” structure formed at...