Topological Quantum Criticality in Superfluids and Superconductors: Surface criticality, Thermal properties, and Lifshitz Majorana fields

TL;DR

This paper explores the quantum critical behavior of topological superfluids and superconductors under symmetry-breaking fields, revealing Lifshitz criticality, surface state transitions, and potential smooth crossovers to trivial phases.

Contribution

It introduces the concept of generalized Lifshitz quantum critical points in topological superfluids and superconductors affected by time reversal symmetry breaking fields.

Findings

Identification of Lifshitz quantum critical points separating gapped and nodal states.

Surface states can exhibit quantum critical behavior near zero TRB fields.

Possible smooth crossover from topological to trivial phases without phase transition.

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 fields with distinct scaling properties. These emergent Lifshitz fields also define finite temperature properties in quantum critical regimes. Moreover, for a certain subset of TRB fields, there exist a precursor to bulk transitions, where surface states can also exhibit quantum critical behavior near zero fields. The possibility for a fully gapped TSF/TSC to smoothly crossover into a topologically trivial state without a phase transition is also examined.