Gap equation with pairing correlations beyond the mean-field approximation and its equivalence to a Hugenholtz-Pines condition for fermion pairs

Year: 2018

Authors: Pisani L., Pieri P., Strinati Calvanese G.

Autors Affiliation: Univ Carnerino, Phys Div, Sch Sci & Technol, I-62032 Carnerino, MC, Italy; INFN, Sez Perugia, I-06123 Perugia, PG, Italy; CNR, INO, Sede Firenze, I-50125 Fi, Italy.

Abstract: The equation for the gap parameter represents the main equation of the pairing theory of superconductivity. Although it is formally defined through a single-particle property, physically, it reflects the pairing correlations between opposite-spin fermions. Here, we exploit this physical connection and cast the gap equation in an alternative form which explicitly highlights these two-particle correlations by showing that it is equivalent to a Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct connection is established in this way between the treatment of the condensate fraction in condensate systems of fermions and bosons. At a practical level, the use of this alternative form of the gap equation is expected to make easier the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept of the new method, we apply the modified form of the gap equation to the long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov correction across the whole BCS-BEC crossover, from the BCS limit of strongly overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for all temperatures in the superfluid phase. Our numerical calculations yield excellent agreement with the recently determined experimental values of the gap parameter for an ultracold Fermi gas in the intermediate regime between BCS and BEC, as well as with the available quantum Monte Carlo data in the same regime.

Journal/Review: PHYSICAL REVIEW B

Volume: 98 (10)      Pages from: 104507-1  to: 104507-23

More Information: We are indebted to C. J. Vale for a discussion about the comparison between the experimental data of Ref. [50] and our theoretical calculations, and to R. Haussmann and W. Zwerger for providing us with the numerical results of the self-consistent t-matrix approximation reported in Fig. 9. This work was partially supported by the Italian MIUR under Contract PRIN-2015 No. 2015C5SEJJ001.
KeyWords: Bcs Superconductivity; Bose-condensation; Crossover; Evolution; Temperature; Transition; Superfluid; Particles; Spectrum; Energy
DOI: 10.1103/PhysRevB.98.104507

Citations: 27
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