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 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 distinguish between the two mechanisms of generating a superconducting gap.

• Received 17 June 2010

DOI:https://doi.org/10.1103/PhysRevB.82.144515