Unconventional critical behavior of fermions hybridized with bosons

TL;DR

This paper investigates the phase transition of fermions hybridized with immobile bosons beyond mean-field theory, revealing unconventional critical behavior and flaws in previous mean-field analyses across different dimensions.

Contribution

It demonstrates that mean-field approximations fail to capture the true critical behavior of the fermion-boson hybrid system, especially in two and three dimensions.

Findings

No Cooper pairing or Bose-condensation in 2D.

No linear term in Ginzburg-Landau expansion in 3D.

Mean-field upper critical field is zero in all dimensions.

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 (3D) 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 dimensions. In particular, the conventional (MFA) upper critical field is zero in any-dimensional BFM.