Topological quantum criticality in superfluids and superconductors: Surface criticality, thermal properties, and Lifshitz Majorana fields

Abstract

Time-reversal-invariant (TRI) topological superfluids (TSFs) and topological superconductors (TSCs) are robust symmetry-protected gapped topological states. In this article, we study the evolution of these topological states in the presence of time-reversal symmetry-breaking (TRB) fields and/or sufficiently large TRI fields. Physically, one of the realizations of TRB fields can be internal spin exchange fields due to background magnetic ordering. We find that the fully gapped TSFs and TSCs are generically separated from other nodal states by various zero temperature quantum critical points that are characterized by generalized quantum Lifshitz Majorana fields with distinct scaling properties. These emergent Lifshitz Majorana fields also define finite temperature properties in quantum critical regimes. Moreover, for a certain subset of TRB fields, there exists a precursor to bulk transitions, where surface states can also exhibit quantum critical behavior near zero fields.

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