Generalized plasma waves in layered superconductors: A unified approach

In a layered and strongly anisotropic superconductor, the hybrid modes provided by propagation of electromagnetic waves in matter identify two well-separated energy scales connected to large in-plane plasma frequency soft out-of-plane Josephson plasmon. Despite wide interest their detection manipulation means different experimental protocols, physical ingredients underlying unified description valid at arbitrary momentum are still poorly understood. Here we provide complete generalized superconductors terms gauge-invariant superconducting phase including both Coulomb interaction relativistic effects. We show that anisotropy superfluid response leads intertwined light-matter with mixed longitudinal transverse character, while purely plasmon is only recovered for wave vectors larger than crossover scale set plasma-frequency anisotropy. Interestingly, below such appear equal weight density response. Our results open promising perspective plasmonic applications made possible next-generation spectroscopic techniques able combine submicron resolution THz resolution.