In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a delta -function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three and
The cold atomic Fermi gas has become the essential paradigm for understanding the crossover between the weak coupling Bardeen-Schrieffer-Cooper (BCS) and strong coupling Bose-Einstein Condensation (BEC) regimes of paired fermion condensates. On tuning the pairing interactions through the crossover, the superfluid condensate becomes maximally robust between the BCS and BEC regimes at what is referred to as the unitary point, giving rise to a maximally peaked phase transition anomaly in the specific heat. We find here, by tracing the jump \Delta\gamma in the electronic specific heat coefficient \gamma at the transition temperature Tc as a function of the gap ratio 2\Delta/kTc, that this same thermodynamic signature occurs in the high-Tc superconducting cuprates. On taking \Delta as the pairing gap in a cold atomic Fermi gas and as the antinodal pseudogap energy in the cuprates, we find \Delta\gamma to be asymmetrically peaked at the same value 2\Delta/kTc~6.5. We show that the observation of this peak in the cuprates, and its coincidence with a normal state maximum in \gamma, provides a previously overlooked thermodynamic signature of condensation at a unitary point.
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.