Phase Transition in Asymmetrical Superconductors

In this paper we study the phase transition in asymmetrical fermion systems. In this scenario the candidates to form pair are particles with mismatched masses and Fermi surfaces. We derive expressions for the determination of the critical temperature in relevant situations for fermionic atom experiments. We argue that an asymmetrical system always undergoes a first order phase transition as a function of the increasing mass and (or) chemical potential asymmetry, except if the constraint $m_a \mu_a=m_b \mu_b$ is imposed.