Robustness of Majorana fermions in proximity-induced superconductors

Abstract

In two-dimensional chiral $p$-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores are protected from the thermal effects by the minigap, ${\ensuremath{\Delta}}^{2}/{ϵ}_{F}$ ($\ensuremath{\Delta}$: bulk gap, ${ϵ}_{F}$: Fermi energy), which is the excitation gap to the higher energy bound states in the vortex cores. Robustness to thermal effects is guaranteed only when $T⪡{\ensuremath{\Delta}}^{2}/{ϵ}_{F}\ensuremath{\sim}0.1\text{ }\text{mK}$, 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 minigaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral $p$-wave superconductor. Specifically, for interfaces with sufficient barrier transparencies, the minigap can be as high as $\ensuremath{\sim}\ensuremath{\Delta}⪢{\ensuremath{\Delta}}^{2}/{ϵ}_{F}$, where $\ensuremath{\Delta}$ is the bulk gap of the $s$-wave superconductor.