Distortional weak-coupling instability of Bogoliubov Fermi surfaces

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 electrons to lattice always leads a weak-coupling instability such state towards spontaneous breaking inversion at low temperatures. This is driven by Cooper logarithm in internal energy but order parameter not superconducting distortional. present comprehensive analysis and introduce measure allows compare strengths competing distortional instabilities. Moreover, we discuss using an effective single-band model. framework reveals duality mapping model maps onto one, providing natural explanation for nature instability. Finally, consider possibility pair-density wave when broken. find it can indeed exist does affect itself.