Density of states of disordered topological superconductor-semiconductor hybrid nanowires

Abstract

Using Bogoliubov-de Gennes equations we numerically calculate the disorder averaged density of states of disordered semiconductor nanowires driven into a putative topological $p$-wave superconducting phase by spin-orbit coupling, Zeeman spin splitting, and the $s$-wave superconducting proximity effect induced by a nearby superconductor. Comparing with the corresponding theoretical self-consistent Born approximation (SCBA) results treating disorder effects, we comment on the topological phase diagram of the system in the presence of increasing disorder. Although disorder strongly suppresses the zero-bias peak (ZBP) associated with the Majorana zero mode, we find some clear remnant of a ZBP even when the topological gap has essentially vanished in the SCBA theory because of disorder. We explicitly compare effects of disorder on the numerical density of states in the topological and trivial phases.