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

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).

v3: Published version. 6+16 pages, 4+22 figures

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• Criticality Across the Energy Spectrum from Random, Artificial Gravitational Lensing in Two-Dimensional Dirac Superconductors
• Fragility of surface states in non-Wigner Dyson topological insulators
• Generalized multifractality at spin quantum Hall transition
• Geodesic geometry of 2+1-D Dirac materials subject to artificial, quenched gravitational singularities
• Hybrid Dispersion Dirac semimetal and Hybrid Weyl phases in Luttinger Semimetals: A dynamical approach
• How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down
• Critical Filaments and Superconductivity in Quasiperiodic Twisted Bilayer Graphene
• Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables