Majorana fermions of a two-dimensional Px+iPy superconductor

TL;DR

This paper investigates Majorana fermions in a two-dimensional p_x+ip_y superconductor by solving the Bogoliubov-de-Gennes equation, revealing how vortex cores support Majorana states and how tunneling conductance can serve as a probe.

Contribution

It provides a detailed analysis of Majorana fermions in a 2D p_x+ip_y superconductor, including their energy dependence and tunneling signatures, which is a novel approach in this context.

Findings

Majorana states in vortex cores have energies decreasing exponentially with sphere radius.

Zero bias conductance peak of antivortex is half that of vortex.

Tunneling conductance can distinguish order parameter symmetry.

Abstract

To investigate Majorana fermionic excitations of a $p_x+ip_y$ superconductor, the Bogoliubov-de-Gennes equation is solved on a sphere for two cases: (i) a vortex-antivortex pair at opposite poles and (ii) an edge near the south pole and an antivortex at the north pole. The vortex cores support a state of two Majorana fermions, the energy of which decreases exponentially with the radius of the sphere, independently of a moderate disorder potential. The tunneling conductance of an electron into the superconductor near the position of a vortex is computed for finite temperature, and is compared to the case of an {\it s}-wave superconductor. The zero bias conductance peak of the antivortex is half that of the vortex. This effect can be used as a probe of the order parameter symmetry, and as a direct measurement of the Majorana fermion.