Boson-fermion model beyond mean-field approximation

TL;DR

This paper analyzes a boson-fermion hybrid model beyond mean-field, revealing that zero-temperature divergences prevent Cooper pairing and that the model cannot explain high-temperature superconductivity, instead resembling a normal metal with damped bosons.

Contribution

It provides an analytical study of the boson-fermion model beyond mean-field, showing the limitations of localized bosons in explaining high-temperature superconductivity.

Findings

Divergent boson self-energy at zero temperature inhibits Cooper pairing.

Boson condensation temperature is below 1K, ruling out high-temperature superconductivity.

Bosonic excitations act as normal impurities with strong damping.

Abstract

A model of hybridized bosons and fermions is studied beyond the mean field approximation. The divergent boson self-energy at zero temperature makes the Cooper pairing of fermions impossible.The frequency and momentum dependence of the self- energy and the condensation temperature $T_{c}$ of initially localized bosons are calculated analytically. The value of the boson condensation temperature $T_{c}$ is below $1K$ which rules out the boson-fermion model with the initially localized bosons as a phenomenological explanation of high-temperature superconductivity. The intra-cell density-density fermion-boson interaction dominates in the fermion self-energy. The model represents a normal metal with strongly damped bosonic excitations. The latter play the role of normal impurities.