We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.
We investigate the specific heat at constant volume
CV in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature
Tc. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a
6Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.
We have studied disorder effects on the coefficients of Ginzburg-Landau expansion for attractive Hubbard model within the generalized DMFT+Σ approximation for the wide region of the values of attractive potential U—from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose-Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature Tc (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of “dirty” superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS–BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at Tc, in BCS–BEC crossover and strong coupling regions.