Reentrant topological phase transitions in a disordered spinless superconducting wire

TL;DR

This paper investigates how disorder causes multiple topological phase transitions in multichannel spinless p-wave superconducting wires, revealing a sequence of trivial and nontrivial phases depending on disorder strength.

Contribution

It demonstrates that multichannel wires undergo multiple topological phase transitions with increasing disorder, with the number of transitions equal to the number of channels, extending previous single-channel results.

Findings

Number of phase transitions equals the number of channels N.

The last transition occurs at a mean free path l = (+1), smaller than the 1D critical value.

Phase transitions alternate between topologically trivial and nontrivial states.

Abstract

In a one-dimensional spinless p-wave superconductor with coherence length \xi, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean free path l=\xi/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean free path l = \xi/(N+1), parametrically smaller than the critical mean free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length \xi.