Ghost Josephson plasmon in bilayer superconductors

The experimental measurement of collective charge fluctuations in metals and superconductors is a preferential tool to benchmark fundamental interactions in solids. Recent experiments in multicomponent systems, from superconducting layered cuprates to multiband metals, highlighted striking effects due to the interplay between different degrees of freedom. In this paper we provide a physical explanation for the existence of a "ghost" Josephson plasmon in bilayer superconductors, layered systems with two layers per unit cells that interact with two different Josephson couplings. We show that one of the two plasmons that emerge after the breaking of the translational symmetry along the out-of-plane direction is connected to counterflowing current fluctuations polarized perpendicularly to the planes. This effect makes it a staggered mode that is virtually transverse at small out-of-plane momenta qc, explaining why it is hidden in the density response at small qc. Our work offers an additional perspective on the understanding of collective excitations in systems with multiple intertwined degrees of freedom.