Characterizing Topological Order in Superconducting Systems

TL;DR

This paper compares two frameworks for understanding superconducting gaps, showing that topological order and symmetry breaking both lead to ground state degeneracy on non-trivial manifolds, and proposes a way to distinguish them via entanglement entropy.

Contribution

It introduces a method to differentiate topological order from symmetry breaking in superconductors using topological entanglement entropy.

Findings

Both mechanisms produce ground state degeneracy on non-trivial manifolds.

Topological entanglement entropy can distinguish between the two mechanisms.

The study provides a unified view of superconducting gap origins.

Abstract

Two established frameworks account for the onset of a gap in a superconducting system: one is based on spontaneous symmetry breaking via the Anderson-Higgs-Kibble mechanism, and the other is based on the recently developed paradigm of topological order. We show that, on manifolds with non trivial topology, both mechanisms yield a degeneracy of the ground state arising only from the {\it incompressibility} induced by the presence of a gap. We compute the topological entanglement entropy of a topological superconductor and argue that its measure allows to {\it distinguish} between the two mechanisms of generating a superconducting gap.