Unconventional critical behaviour of fermions hybridized with bosons

A phase transition into the condensed state of fermions hybridized with immobile bosons is examined beyond the ordinary mean-field approximation (MFA) in two and three dimensions. The hybridization interaction does not provide the Cooper pairing of fermions and the Bose condensation in two dimensions. In the three-dimensional boson–fermion model (BFM), an expansion in the strength of the order parameter near the transition yields no linear homogeneous term in the Ginzburg–Landau–Gor’kov equation. This indicates that previous mean-field discussions of the model are flawed in any dimension. In particular, the conventional (MFA) upper critical field is zero in any-dimensional BFM.