Anapole superconductivity from $\mathcal{PT}$-symmetric mixed-parity interband pairing

TL;DR

This paper explores how mixed-parity superconducting states that break time-reversal symmetry can exhibit asymmetric quasiparticle spectra and anapole moments, leading to novel nonuniform superconducting states in multiband systems.

Contribution

It introduces the concept of anapole moments in superconductors arising from nonunitary interband pairing, extending the idea of anapole order to superconducting states.

Findings

Asymmetric Bogoliubov spectra occur in certain mixed-parity superconductors.

Anapole moments stabilize nonuniform Fulde-Ferrell-Larkin-Ovchinnikov states.

Relevance to multiband superconductors like UTe$_2$.

Abstract

Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliubov spectrum. We also demonstrate that the asymmetric Bogoliubov quasiparticles lead to the effective anapole moment of the superconducting state, which stabilizes a nonuniform Fulde-Ferrell-Larkin-Ovchinnikov state at zero magnetic fields. The concept of anapole order employed in nuclear physics, magnetic materials science, strongly correlated electron systems, and optoelectronics is extended to superconductors by this work. Our conclusions are relevant for any multiband superconductors with competing even- and odd-parity pairing channels. Especially, we discuss the superconductivity in UTe$_2$.