Relativistic BCS-BEC crossover at zero temperature

We investigate the BCS-BEC (Bardeen-Cooper-Shriffer-Bose-Einstein condensation) crossover at zero temperature in the frame of a relativistic model. The universality of the BCS-BEC crossover for nonrelativistic systems breaks down in the relativistic case and the crossover can be induced by changing the density. When the effective scattering length is much less than the fermion Compton wavelength, we recover the nonrelativistic result if the gas is initially in a nonrelativistic state. At ultrastrong coupling where the scattering length is of the order of the Compton wavelength, a new BEC state appears. In this state the condensed bosons become nearly massless and antifermions are excited. The behavior of the Goldstone mode and the mixing between the amplitude and phase modes are significantly different in different condensed regions.