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

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.