Bardasis-Schrieffer-like phase mode in a superconducting bilayer

We theoretically study the low-lying collective modes of an even-parity spin-singlet superconducting bilayer, where strong spin-orbit coupling leads to a closely competing odd-parity pairing state. We develop a gauge-invariant theory for the coupling of phase fluctuations to an external electromagnetic field and show that the competing odd-parity pairing instability gives rise to a Bardasis-Schrieffer-like phase mode within the excitation gap. Accounting for the long-range Coulomb interaction, however, we find that this mode is converted into an antisymmetric plasmon and is likely pushed into the quasiparticle continuum.