An Overview of the Andreev Crossed Re?ection-A Majorana Path Integral Approach

Abstract

We investigate the effect of the Majorana Fermions which are formed at the boundary of a p-wave superconductor. When the Majorana overlapping energy is ?nite we construct the scattering matrix S by maping the Majorana zero mode to Fermions for which coherent states are de?ned and a path integral is obtained. The path integral is used to compute the scattering matrix in terms of the electrons in the leads. This method is suitable for computing the conductivity. We investigate a chiral Majorana Hamiltonian and show that in the absence of vortices the conductivity vanish. We compute the conductivity for p wave superconductor coupled to two metallic leads we show that when the overlapping energy between the two Majorana fermions is ?nite the Andreev Crossed re?ection conductance is ?nite.