Screening masses of photons interacting with a two-species fermionic system in relativistic BCS-BEC crossover

We address the behavior of Debye and Meissner masses of photons in a condensate of fermion pairs in the presence of number density asymmetry. Our formalism applies to a two-species fermionic system with number density asymmetry in BCS-Bose-Einstein condensation (BEC)relativistic BEC crossover and with variable rapidity. Our results recover the known results of the photon self-energy in the ultrarelativistic limit and the superfluid density in the nonrelativistic limit. We further consider the electromagnetic stability of the condensate and show that the Meissner mass squared can become negative in the weakly coupling BCS regime and the strongly coupling relativistic BEC regime. The electromagnetic instability is compared to the mechanical stability discussed in previous works.