We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.
We study the phase diagram of two-dimensional Bose-Fermi mixtures of ultracold atoms on a triangular optical lattice, in the limit when the velocity of bosonic condensate fluctuations is much larger than the Fermi velocity. We contrast this work with our previous results for a square lattice system in the work of Mathey et al. [Phys. Rev. Lett. 97, 030601 (2006)]. Using functional renormalization-group techniques we show that the phase diagrams for a triangular lattice contain exotic superconducting phases. For spin-
1∕2 fermions on an isotropic lattice we find a competition of
s-,
p-, extended
d-, and
f-wave symmetries, as well as antiferromagnetic order. For an anisotropic lattice, we further find an extended
p-wave phase. A Bose-Fermi mixture with spinless fermions on an isotropic lattice shows a competition between
p- and
f-wave symmetries. These phases can be traced back to the geometric shapes of the Fermi surfaces in various regimes, as well as the intrinsic frustration of a triangular lattice.