BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids

TL;DR

This review explores the BCS-BEC crossover, focusing on finite temperature effects, pseudogap phenomena, and their relevance to high-temperature superconductors and ultracold atomic gases, highlighting theoretical approaches and experimental implications.

Contribution

It provides a comprehensive analysis of finite temperature effects in the BCS-BEC crossover, connecting high-Tc superconductivity with ultracold gases, and evaluates various T-matrix theoretical methods.

Findings

Pseudogap state can be understood via BCS-BEC crossover.

Preformed pairs exist above the superconducting transition.

T-matrix approaches are consistent with fluctuation theories.

Abstract

We review the BCS to Bose Einstein condensation (BEC) crossover scenario which is based on the well known crossover generalization of the BCS ground state wavefunction $\Psi_0$. While this ground state has been summarized extensively in the literature, this Review is devoted to less widely discussed issues: understanding the effects of finite temperature, primarily below $T_c$, in a manner consistent with $\Psi_0$. Our emphasis is on the intersection of two important problems: high $T_c$ superconductivity and superfluidity in ultracold fermionic atomic gases. We address the "pseudogap state" in the copper oxide superconductors from the vantage point of a BCS-BEC crossover scenario, although there is no consensus on the applicability of this scheme to high $T_c$. We argue that it also provides a useful basis for studying atomic gases near the unitary scattering regime; they are most likely in the counterpart pseudogap phase. That is, superconductivity takes place out of a non-Fermi liquid state where preformed, metastable fermion pairs are present at the onset of their Bose condensation. As a microscopic basis for this work, we summarize a variety of $T$-matrix approaches, and assess their theoretical consistency. A close connection with conventional superconducting fluctuation theories is emphasized and exploited.