Majorana fermions of a two-dimensional Px+iPy superconductor

Abstract

To investigate Majorana fermionic excitations of a $p_x+i{p}_y$ 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.

15 pages, 17 figures

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• $AbInitio$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors
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