Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover

Abstract

The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc obtained when neglecting screening effects. Subsequent work on this topic, aimed at extending the original GMB argument away from the BCS limit with diagrammatic methods, has kept this disentangling between pairing and screening throughout the BCS-BEC crossover, without realising that the conditions for it to be valid are soon violated away from the BCS limit. Here, we reconsider this problem from a more general perspective and argue that pairing and screening are intrinsically entangled with each other along the whole BCS-BEC crossover but for the BCS limit considered by GMB. We perform a detailed numerical calculation of the GMB diagrammatic contribution extended to the whole BCS-BEC crossover, where the full wave-vector and frequency dependence occurring in the repeated in-medium two-particle scattering is duly taken into account. Our numerical calculations are tested against analytic results available in both the BCS and BEC limits, and the contribution of the GMB diagrammatic term to the scattering length of composite bosons in the BEC limit is highlighted. We calculate Tc throughout the BCS-BEC crossover and find that it agrees quite well with Quantum Monte Carlo calculations and experimental data available in the unitarity regime.

21 pages, 11 figures

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• BCS-BEC crossover at finite temperature in the broken-symmetry phase
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• Goldstone mode and pair-breaking excitations in atomic Fermi superfluids
• Critical Temperature Curve in the BEC-BCS Crossover
• Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
• Particle-hole fluctuations in the BCS-BEC Crossover
• Superfluid pairing between fermions with unequal masses
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• Induced interactions for ultracold Fermi gases in optical lattices
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• Screening and anti-screening of the pairing interaction in low-density neutron matter
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• Precursor of Superfluidity in a Strongly Interacting Fermi Gas with Negative Effective Range
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• Tunneling study in granular aluminum near the Mott metal-to-insulator transition
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• Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasi-flat band: Enhanced critical temperature evading particle-hole fluctuations
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• Detecting the phase transition in a strongly-interacting Fermi gas by unsupervised machine learning
• The Gor'kov and Melik-Barkhudarov correction to an imbalanced Fermi gas in the presence of impurities
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• Temporal fluctuation induced order in conventional superconductors
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