Abstract

In order to investigate Majorana bound states in p-wave superconductors and to reveal the precise influence of boundaries and inhomogeneities on the local structure of competing superconducting order parameters, we solve inhomogeneous Bogoliubov-de Gennes equations. Going beyond the quasi-classical approach we examine in particular the role of Friedel-oscillations due to inhomogeneities and the surface of the superconductor and analyse the distinct behaviour of the p-wave and the surface induced s-wave pairing amplitudes. In order to demonstrate the experimental accessibility of the occurring spatial oscillations in the singlet order parameter we show that this signature transports into the Josephson current measured in a superconducting scanning tunneling microscopy.