Unconventional critical behaviour of fermions hybridized with bosons

Abstract

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.

Acknowledgements

I greatly appreciate enlightening discussions with A. F. Andreev, V. V. Kabanov, A. P. Levanyuk, R. Micnas and S. Robaszkiewicz, and the support of the Leverhulme Trust (UK) via grant F/00261/H.