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

We study bound states in an s-wave superconducting strip on the surface of a topological superconductor with the perpendicular Zeeman field. We prove analytically that an arbitrarily small local perturbation of the Zeeman field generates Andreev bound states with energies near the superconducting gap edges, while the (nonmagnetic) impurity potential does not produce such an effect. Rather large perturbations of the Zeeman field can lead to the appearance of Andreev bound states with energies near zero. We analytically find wave functions of the Andreev bound states under consideration. In contrast to the one-dimensional case, the wave functions do not satisfy the conjugation conditions that are characteristic of Majorana states because of the influence of neighboring subbands.