To close or not to close: the fate of the superconducting gap across the topological quantum phase transition in Majorana-carrying semiconductor nanowires

TL;DR

This paper theoretically examines the behavior of the superconducting gap in Majorana-carrying semiconductor nanowires near a topological quantum phase transition, explaining why gap closure signatures are often not observed experimentally.

Contribution

It demonstrates that the local density of states at the wire's end does not universally show gap closure at the transition, clarifying experimental observations.

Findings

End-of-wire LDOS dependence on magnetic field is non-universal.

Signatures of gap closing are often invisible in experiments.

Provides explanation for non-observation of gap closure in recent experiments.

Abstract

We investigate theoretically the low energy physics of semiconductor Majorana wires in the vicinity of a magnetic field-driven topological quantum phase transition (TQPT). The local density of states (LDOS) at the end of the wire, which is directly related to the differential conductance in the limit of point-contact tunneling, is calculated numerically. We find that the dependence of the end-of-wire LDOS on the magnetic field is non-universal and that the signatures associated with the closing of the superconducting gap at the Majorana TQPT are essentially invisible within a significant range of experimentally relevant parameters. Our results provide an explanation for the recent observation of the apparent non-closure of the gap at the Majorana TQPT in semiconductor nanowires.