Condensate fraction in metallic superconductors and ultracold atomic vapors

TL;DR

This paper analyzes the condensate density and fraction in superconductors and ultracold atomic vapors using BCS theory, providing analytical formulas and exploring temperature and coupling effects.

Contribution

It offers a detailed analytical study of condensate properties in superconductors and compares them with ultracold Fermi gases, highlighting similarities and differences.

Findings

Derived analytical formula for zero-temperature condensate density.

Calculated condensate fraction for various metals.

Explored temperature dependence and electron-phonon coupling effects.

Abstract

We investigate the condensate density and the condensate fraction of conduction electrons in weak-coupling superconductors by using the BCS theory and the concept of off-diagonal-long-range-order. We discuss the analytical formula of the zero-temperature condensate density of Cooper pairs as a function of Debye frequency and energy gap, and calculate the condensate fraction for some metals. We study the density of Cooper pairs also at finite temperature showing its connection with the gap order parameter and the effects of the electron-phonon coupling. Finally, we analyze similarities and differences between superconductors and ultracold Fermi atoms in the determination of their condensate density by using the BCS theory.