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Physics Essays

A Survey on the Crossover from BCS Superconductivity to Bose‐Einstein Condensation

Giancarlo Calvanese Strinati

Published Sep 1, 2000• 7 citations
Publisher

Abstract

The BCS superconductivity instability of a Fermi system (due to an attractive interparticle interaction) ...
DOI
10.4006/1.3028840

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The crossover from weak-coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that have realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. Although our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport, and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics—quark-gluon plasmas, gauge-gravity duality, and high-temperature superconductivity—and conclude with open questions about strongly interacting Fermi gases.
The self-consistent equations, which have been derived recently as a microscopic model for the crossover between BCS superconductivity and Bose-Einstein condensation in a three-dimensional interacting Fermi system [R. Haussmann, Z. Phys. B 91, 291 (1993)], are solved numerically by repeated Fourier transformation. We find a superfluid transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ which increases monotonically with increasing attractive coupling strength. Furthermore, we determine the chemical potential \ensuremath{\mu}, the fermion distribution function n(k), and the complex effective mass 2m∗{\mathit{m}}^{\mathrm{*}}m∗ of the fermion pairs at T=Tc{\mathit{T}}_{\mathit{c}}Tc​. The bound fermion pairs cause a power-law tail \ensuremath{\sim}${\mathit{k}}^{\mathrm{\ensuremath{-}}4}$ in n(k) for large k and behave as short-living quasiparticles in the crossover region, which is indicated by a large imaginary part of 2m∗{\mathit{m}}^{\mathrm{*}}m∗.