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 nontopological 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^2/h $, with occasional disorder-dominated peaks exceeding $ 2e^2/h $. We present animations of the simulated crossover behavior and discuss experimental implications. Additionally, in order to simulate the realistic disorder in experimental nanowires, we also study in depth the case of disorder arising from random individual static impurities along the wire, and consider crossover associated with such impurity effects. Our results, when compared qualitatively with existing Majorana nanowire experimental results, indicate the dominant role of random disorder in the experiments. It turns out that all three mechanisms may produce trivial zero-bias peaks in the tunnel conductance, and the crossover among these physical mechanisms (i.e., when more than one mechanism is present in the system) is smooth and continuous, making it difficult a priori to conclude which mechanism is dominant in a particular sample just by a casual inspection of the zero-bias conductance peaks.