Estimating disorder and its adverse effects in semiconductor Majorana nanowires

TL;DR

This paper estimates the disorder levels in semiconductor nanowires used for Majorana zero mode experiments, finding current disorder is too high for topological Majorana modes and explaining the sporadic experimental observations.

Contribution

It provides a dataset of disorder estimates from literature and links these to the emergence of trivial zero modes in Majorana nanowire simulations.

Findings

Current disorder exceeds the threshold for topological Majorana modes by at least an order of magnitude.

Disorder leads to trivial zero-bias peaks that can be fine-tuned and occasionally observed in experiments.

Most disordered systems show no significant features in tunnel spectra, aligning with experimental results.

Abstract

We use the available transport measurements in the literature to develop a dataset for the likely amount of disorder in semiconductor (InAs and InSb) materials which are used in fabricating the superconductor-semiconductor nanowire samples in the experimental search for Majorana zero modes. Using the estimated disorder in direct Majorana simulations, we conclude that the current level of disorder in semiconductor Majorana nanowires is at least an order of magnitude higher than that necessary for the emergence of topological Majorana zero modes. In agreement with existing results, we find that our estimated disorder leads to the occasional emergence of trivial zero modes, which can be post-selected and then further fine-tuned by varying system parameters (e.g., tunnel barrier), leading to trivial zero-bias conductance peaks in tunneling spectroscopy with $ \sim 2e^2/h $ magnitude. Most calculated tunnel spectra in these disordered systems, however, manifest essentially no significant features, which is also consistent with the current experimental status, where zero-bias peaks are found only occasionally in some samples under careful fine-tuning.