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

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 simultaneously broken. This work shows that symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due nonunitary interband pairing. For generic two-band models, we derive necessary conditions for spectrum. We also demonstrate quasiparticles lead effective anapole moment of state, which stabilizes a nonuniform Fulde-Ferrell-Larkin-Ovchinnikov state at zero magnetic fields. The concept order employed in nuclear physics, materials science, strongly correlated electron systems, optoelectronics extended superconductors by this work. Our conclusions relevant any multiband competing even- odd-parity pairing channels. Especially, discuss UTe$_2$.