Critical Percolation Without Fine Tuning on the Surface of a Topological Superconductor

TL;DR

This paper provides numerical evidence that surface states of a topological superconductor naturally sit at a quantum Hall transition point without fine-tuning, showing universal delocalization properties across energies.

Contribution

It demonstrates that finite-energy surface states of a topological superconductor are delocalized and exhibit universal statistics, independent of the winding number, aligning with the spin quantum Hall transition.

Findings

Finite-energy surface states are delocalized.

Surface states exhibit universal statistics.

States are at a quantum Hall plateau transition.

Abstract

We present numerical evidence that most two-dimensional surface states of a bulk topological superconductor (TSC) sit at an integer quantum Hall plateau transition. We study TSC surface states in class CI with quenched disorder. Low-energy (finite-energy) surface states were expected to be critically delocalized (Anderson localized). We confirm the low-energy picture, but find instead that finite-energy states are also delocalized, with universal statistics that are independent of the TSC winding number, and consistent with the spin quantum Hall plateau transition (percolation).