The Andreev crossed reflection -a Majorana path integral approach

TL;DR

This paper develops a path integral approach to analyze Majorana fermions at p-wave superconductor boundaries, revealing conditions under which crossed Andreev reflection conductance is finite.

Contribution

It introduces a novel path integral method mapping Majorana zero modes to fermions, enabling computation of scattering matrices and conductance in superconductor-lead systems.

Findings

Conductivity vanishes without vortices.

Finite overlapping energy yields finite crossed Andreev reflection.

Method applicable for computing superconductor conductance.

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 finite we construct the scattering matrix $\mathbf{S}$ by maping the Majorana zero mode to Fermions for which coherent states are defined 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 finite the Andreev Crossed reflection conductance is finite.