Distortional weak-coupling instability of Bogoliubov Fermi surfaces

TL;DR

This paper demonstrates that electron-lattice coupling causes a weak-coupling instability in Bogoliubov Fermi surfaces of centrosymmetric multiband superconductors, leading to spontaneous inversion symmetry breaking through a distortional order.

Contribution

It introduces a comprehensive symmetry analysis and a measure to compare distortional instabilities, revealing a duality mapping that explains the weak-coupling nature of the instability.

Findings

Weak-coupling instability driven by Cooper logarithm

Distortional order parameter not superconducting

Pair-density wave state can exist without affecting the instability

Abstract

Centrosymmetric multiband superconductors which break time-reversal symmetry generically have two-dimensional nodes, i.e., Fermi surfaces of Bogoliubov quasiparticles. We show that the coupling of the electrons to the lattice always leads to a weak-coupling instability of such a state towards spontaneous breaking of inversion symmetry at low temperatures. This instability is driven by a Cooper logarithm in the internal energy but the order parameter is not superconducting but distortional. We present a comprehensive symmetry analysis and introduce a measure that allows to compare the strengths of competing distortional instabilities. Moreover, we discuss the instability using an effective single-band model. This framework reveals a duality mapping of the effective model which maps the distortional order parameter onto a superconducting one, providing a natural explanation for the Cooper logarithm and the weak-coupling nature of the instability. Finally, we consider the possibility of a pair-density wave state when inversion symmetry is broken. We find that it can indeed exist but does not affect the instability itself.