Abstract
BCS–Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Here we study the effect of the (often dropped) particle-hole channel on the zero T gap Δ(0), superfluid transition temperature Tc, the pseudogap at Tc, and the mean-field ratio 2Δ(0)/, from BCS through BEC regimes, using a pairing fluctuation theory which includes self-consistently the contributions of finite-momentum pairs and features a pseudogap in single particle excitation spectrum. Summing over the infinite particle-hole ladder diagrams, we find a complex dynamical structure for the particle-hole susceptibility χph, and conclude that neglecting the self-energy feedback causes a serious over-estimate of χph. While our result in the BCS limit agrees with Gor’kov et al., the particle-hole channel effect becomes more complex and pronounced in the crossover regime, where χph is reduced by both a smaller Fermi surface and a big (pseudo)gap. Deep in the BEC regime, the particle-hole channel contributions drop to zero. We predict a density dependence of the magnetic field at the Feshbach resonance, which can be used to quantify χph and test different theories.
Highlights
Lowest order induced interaction is not appropriate away from the weak coupling BCS regime
There was necessarily no pseudogap in the fermion excitation spectrum at Tc. This is basically equivalent to replacing the particle-hole susceptibility χp0h by an essentially temperature independent constant, leading to a simple downshift in the pairing interaction
Experimental evidence for its existence comes from high Tc superconductors[13,28,37,38,39] as well as atomic Fermi gases[40,41,42,43,44]
Summary
BCS–Bose-Einstein condensation (BEC) crossover is effected by increasing pairing strength between fermions from weak to strong in the particle-particle channel, and has attracted a lot of attention since the experimental realization of quantum degenerate atomic Fermi gases. Self-consistently including the self-energy feedback is important For both levels of average, we find that while in the BCS limit, the particle-hole channel effect may be approximated by a downshift in the pairing strength so that the ratio 2Δ(0)/Tc is unaffected, the situation becomes more complex as the interaction becomes stronger where the gap is no longer very small. These plots reveal that by neglecting the feedback effect, the bare χp0h (P) misses important interesting dynamic structures associated with the pseudogap, which leads to a low frequency gap in χp′h′ (ν, 0).
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