Majorana states in a p-wave superconducting ring

Abstract

The spectrum of excitations of the chiral superconducting ring with internal and external radii R-i, R-e (comparable with coherence length xi) trapping a unit flux Phi(0) is calculated. We find within the Bogoliubov-de Gennes approach that there exists a pair of precisely zero-energy states when 2k(perpendicular to)(R-e - R-i)/pi is integer (here k(perpendicular to) is the momentum component in the disk plane while k(perpendicular to) xi > 1). They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon. Copyright (C) EPLA, 2013