It has long been known that the critical temperature of a BCS weak-coupling superfluid gets considerably reduced when the Gorkov-Melik-Barkhudarov (G-MB) correction is considered, whereby particle-hole excitations affect the two-fermion scattering in the medium responsible the formation of Cooper pairs. Here, by a careful analysis which takes into account the wave-vector and frequency dependence of the pair propagator (which gets increasingly important away from the weak coupling limit where the G-MB correction was originally derived) we extend the effects of the G-MB correction throughout the BCSBEC crossover. In particular, the Feynman diagram responsible for the G-MB correction is inserted in a partially self-consistent T-matrix scheme; the resulting equations are solved numerically and yield a curve for the critical temperature which agrees very well with the Quantum Monte Carlo data available in the crossover region.
In a superfluid system, off-diagonal long-range order is expected to be exhibited in the appropriate reduced density matrices when the relevant particles (either bosons or fermion pairs) are considered to recede sufficiently far apart from each other. This concept is usually exploited to identify the value of the condensate density, without explicit concern, however, as to the spatial range over which this asymptotic condition can effectively be achieved. Here, based on a diagrammatic approach that includes beyond-mean-field pairing fluctuations in the broken-symmetry phase at the level of the
t-matrix also with the inclusion of the Gorkov-Melik-Barkhudarov (GMB) correction, we present a systematic study of the two-particle reduced density matrix for a superfluid fermionic system undergoing the BCS-BEC crossover, when the entities to recede far apart from each other evolve with continuity from largely overlapping Cooper pairs in the BCS limit to dilute composite bosons in the BEC limit. By this approach, we not only provide the coupling and temperature dependence of the condensate density at the level of our diagrammatic approach, which includes the GMB correction, but we also obtain the evolution of the spatial dependence of the two-particle reduced density matrix, from a power law at low temperature to an exponential dependence at high temperature in the superfluid phase, when the interparticle coupling spans the BCS-BEC crossover. Our results put limitations on the minimum spatial extent of a finite-size system for which superfluid correlations can effectively be established.
We investigate the phase diagram of two-component fermions in the BCS-BEC (Bose-Einstein condensate) crossover. Using functional renormalization-group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wave-function renormalization, an effective Fermi radius, and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second-order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkov's correction for a small negative scattering length
a and with an interacting Bose gas for a small positive
a. At the unitarity point the result for the gap at zero temperature agrees well with quantum Monte Carlo simulations, while the critical temperature differs.