Effects of the GMB correction on the critical temperature and gap parameter throughout the BCS-BEC crossover

It has long been known that the critical temperature and gap parameter of a BCS weak-coupling superfluid are considerably reduced by the inclusion of the Gorkov-Melik-Barkhudarov (G-MB) correction, whereby particle-hole excitations screen the two-fermion effective interaction in the medium. We have extended the effects of the G-MB correction throughout the whole BCS-BEC crossover by identifying the Feynman diagrams responsible for the G-MB correction in both the normal and superfluid phases. The numerical solution of the resulting equations yield results for the critical temperature and gap which agree very well with Quantum Monte Carlo and experimental data in the crossover region