Majorana-metal transition in a disordered superconductor: percolation in a landscape of topological domain walls

TL;DR

This paper demonstrates that increasing electrostatic disorder in a disordered chiral p-wave superconductor induces a transition to a Majorana metal phase via percolation of topological domain walls, with a constructed network revealing the phase diagram.

Contribution

It introduces a numerical method using the spectral localizer to map topological domain walls and links their percolation to the Majorana metal transition.

Findings

Percolation of domain walls causes the phase transition.

Constructed network reveals the thermal metal-insulator phase diagram.

Disorder strength controls the topological phase transition.

Abstract

Most superconductors are thermal insulators. A disordered chiral $\textit{p}$-wave superconductor, however, can make a transition to a thermal metal phase. Because heat is then transported by Majorana fermions, this phase is referred to as a Majorana metal. Here we present numerical evidence that the mechanism for the phase transition with increasing electrostatic disorder is the percolation of boundaries separating domains of different Chern number. We construct the network of domain walls using the spectral localizer as a ``topological landscape function'', and obtain the thermal metal--insulator phase diagram from the percolation transition.