Crossover between trivial zero modes in Majorana nanowires

Abstract

We consider the superconductor-semiconductor nanowire hybrid Majorana platform (“Majorana nanowire”) in the presence of a deterministic spatially slowly varying inhomogeneous chemical potential and a random spatial quenched potential disorder, both of which are known to produce non-topological almost-zero energy modes mimicking the theoretically predicted topological Majorana zero modes. We study the crossover among these mechanisms by calculating the tunnel conductance while varying the relative strength between inhomogeneous potential and random disorder in a controlled manner. We find that the entire crossover region manifests abundant trivial zero modes, many of which showing the apparent ‘quantization’ of the zero-bias conductance peak at 2e/h, with occasional disorder-dominated peaks exceeding 2e/h. We present animations of the simulated crossover behavior, and discuss experimental implications. Our results, when compared qualitatively with existing Majorana nanowire experimental results, indicate the dominant role of random disorder in the experiments.