15 - Crossover from BCS Theory to Bose–Einstein Condensation

Summary

Abstract

This article gives a detailed review of our current theoretical understanding of the crossover from cooperative Cooper pairing to independent bound-state formation and Bose–Einstein condensation in Fermi systems with increasing attractive interactions.

Introduction

There are two well-known paradigms for understanding the phenomena of superconductivity and superfluidity:

1. (I) BCS theory [1], in which the normal state is a degenerate Fermi liquid that undergoes a pairing instability at a temperature T_c ≪ ε_f, the degeneracy scale. The formation of Cooper pairs and their condensation (macroscopic occupation of a single quantum state) both occur simultaneously at the transition temperature T_c.

2. (II) Bose–Einstein condensation (BEC) of bosons at a T_c of the order of their degeneracy temperature. At a fundamental level these bosons (for example, ⁴He or excitons) are invariably composite objects made up of an even number of fermions. The composite particles form at some very high temperature scale of the order of their dissociation temperature T_dissoc, and these “pre-formed” bosons then condense at the BEC T_c ≪ T_dissoc.

In most cases of experimental interest the system under consideration clearly falls into one category or the other. For instance, ³He is a Fermi superfluid described by (I) whereas ⁴He is a Bose superfluid (II). Essentially all cases of superconductivity in metals that we understand reasonably well are much closer to (I) than to (II), as evidenced by the existence of fermionic quasiparticles above T_c.