Superfluidity in Two-Dimensional Imbalanced Fermi Gases

We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy $\epsilon_B$, whose variation allows to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance $h_c$ after which there is a first-order phase transition to the normal state. We find that $h_c$, the Chandrasekhar-Clogston limit of superfluidity, has the same value as in three dimensional systems. We show that for a fixed ratio $\epsilon_B/\epsilon_F$, where $\epsilon_F$ is the two-dimensional Fermi energy, as the density imbalance $m$ is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance $m_c$ phase separation is not supported and the normal phase is energetically preferable. The BCS-BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.