Plasma waves in layered superconductors

Plasmons represent the fundamental excitations of the conduction electrons in a metal, visible in the density response. In a superconductor the plasmon controls also the spectrum of the superconducting phase mode. In layered cuprates the weak Josephson coupling among planes and the gapping out of the quasiparticle continuum below the gap makes it possible to observe a soft and undamped out-of-plane plasmon, with a high potential for nanophotonic THz applications. At the same time, recent measurements of the high-energy in-plane plasmon showed a rather strong damped mode. Despite the strong interest in plasmonic applications, a full theoretical description linking the soft plasmon to the high-energy in-plane plasmon at arbitrary momentum is missing. Here I show how the fundamental mixing among longitudinal and transverse excitations in a layered system reflects in the dispersion of the plasma waves, and how the low-frequency limit can be connected to the high-frequency one [1]. Finally, I will also review recent progresses in the understanding of the non-linear THz response triggered by two-plasmon excitations in cuprates [2].