Generalized plasma waves in layered superconductors: A unified approach

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