Robustness of Majorana fermions in 2D topological superconductors

Abstract

In 2D chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores follow non-Abelian statistics which can be potentially exploited to build a topological quantum computer. The Majorana states are protected from the thermal effects by the mini-gap, $\Delta^2/\epsilon_F$ ($\Delta$:bulk gap, $\epsilon_F$: Fermi energy), which is the excitation gap to the higher-energy, non-topological, bound states in the vortex cores. Robustness to thermal effects is guaranteed only when $T \ll \Delta^2/\epsilon_F \sim 0.1$ mK, which is a very severe experimental constraint. Here we show that when s-wave superconductivity is proximity-induced on the surface of a topological insulator or a spin-orbit-coupled semiconductor, as has been recently suggested, the mini-gaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral p-wave superconductor. Specifically, for interfaces with high barrier transparencies, the mini-gap can be as high as $\sim \Delta \gg \Delta^2/\epsilon_F $, where $\Delta$ is the bulk gap of the s-wave superconductor responsible for the proximity effect.