A Simple Model of Superconductors: Insights from Free Fermion and Boson Gases

TL;DR

This paper presents a simplified model of superconductors using free fermion and boson gases to analyze the temperature dependence of Cooper pair formation, aiming to shed light on high-temperature superconductivity mechanisms.

Contribution

It introduces a straightforward model combining Fermi and Bose gases to study superconducting properties and their temperature dependence.

Findings

Computed the temperature dependence of Cooper pair ratio $2 r(T) / N$

Provided insights into high-temperature superconductivity mechanisms

Analyzed coherence in Cooper pairs across different superconductors

Abstract

Superconductors at temperatures below the critical temperature $T_c$ can be modeled as a mixture of Fermi and Bose gases, where the Fermi gas consists of conduction electrons and the Bose gas comprises Cooper pairs. This simple model enables the computation of the temperature dependence of $2 r(T) / N$, where $N$ is the total number of conduction electrons and $r(T)$ is the number of Cooper pairs at temperature $T$. Analyzing $2 r(T) / N$ across various superconductors may provide significant insights into the mechanisms behind high-temperature superconductivity, especially regarding coherence in Cooper pairs.