Axionic $p + is$ superconductivity from two pairing channels

In unconventional superconductors, inversion and/or time-reversal symmetries may be broken, either extrinsically or spontaneously. Here, we consider a simple BCS model with both attractive singlet and attractive triplet pairing channels. We show that when the triplet instability dominates, the model predicts an axionic superconducting state, in which both inversion and time-reversal symmetries are spontaneously broken by the superconductivity without requiring spin-orbit coupling. This leads to characteristic experimental signatures of spontaneous symmetry breaking in superconductors, such as a two-step transition in the specific heat. We critically analyze whether familiar pairing mechanisms such as the electron-phonon interaction and ferromagnetic spin fluctuations could produce such an axionic state.