Instabilities in fermions and BEC mixtures

We study instabilities in a mixture of interacting fermionic and bosonic ultra-cold atoms. We focus on BCS transitions of the fermions that can be generated from attractive interactions mediated by bosons that are in a BEC phase. We study the p-wave instability [1] for indistinguishable (single spin) fermions in detail, taking into account the dynamical part of the mediated interaction. We employ a functional renormalization-group approach that takes retardation effects into account [2], calculate the renormalized interaction vertices and self-energies for this system, and obtain the phase diagram, sub-dominant instabilities, and transition temperatures, giving estimates for realistic parameters. We also investigate what happens in this system close to the phase-separation transition [3], and explore other possible fermionic phases, including fermion BCS pairings with other pairing symmetries. \\[4pt] [1] D. V. Efremov and L. Viverit, Phys. Rev. B {\bf 65}, 134519 (2002)\\[0pt] [2] S.-W. Tsai {\it et al.}, Phys. Rev. B {\bf 72}, 054531 (2005)\\[0pt] [3] D. H. Santamore and E. Timmermans, Phys. Rev. A {\bf 78}, 013619 (2008)