Partially separated Majorana modes in a disordered medium

Abstract

Focusing on the implications of recent experiments on Majorana zero modes in semiconductor-superconductor (SM-SC) heterostructures, we critically examine the quantization of the zero-bias differential conductance as a possible unambiguous signature of Majorana physics in the presence of disorder. By numerically calculating the zero-bias conductance (ZBC) maps as function of Zeeman splitting and chemical potential for different disorder realizations, we find that the large topological region associated with the clean system, which is characterized by a quantized ZBC height $2{e}^{2}/h$, breaks up into progressively smaller ``islands'' as the disorder strength increases. For strong disorder we show that the presence of small islands with ZBC value (approximately) equal to $2{e}^{2}/h$, which we refer to as ``quantized islands,'' represents a unique signature of Majorana physics supporting partially separated Majorana modes (ps-MMs). Because of the small area/volume of these quantized islands in the parameter space, observing them in experiments may require sample selection and the systematic scanning of a large volume in the control parameter space. Upon decreasing disorder, the quantized islands increase in size and eventually coalesce into large topological regions. We conclude that the observation of quantized islands with ZBC value approximately equal to $2{e}^{2}/h$ demonstrates unambiguously the presence of the key ingredients necessary for Majorana physics, provides an excellent diagnostic tool for evaluating the disorder strength, and, consequently, represents the next natural milestone in Majorana search.