  We investigate chiral symmetry breaking in a model of Dirac fermions with a
complexified coupling constant whose imaginary part represents dissipation. We
introduce a chiral chemical potential and observe that for real coupling a
relativistic BCS-BEC crossover is realized. We solve the model in the
mean-field approximation and construct the phase diagram as a function of the
complex coupling. It is found that the dynamical mass increases under
dissipation, although the chiral symmetry gets restored if dissipation exceeds
a threshold.
