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arXiv:cond-mat/0106250 · Physical review. B, Condensed matter

Cooper pairing with finite angular momentum via a central attraction: From the BCS to the Bose limits

Jorge Quintanilla, Balazs L. Gyorffy, James F. Annett, J. P. Wallington

Published Dec 31, 2002• 10 citations
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Abstract

In the context of a simple model featuring an explicit, central interaction potential, and using a standard functional-integral technique, we study superconductivity with angular momentum quantum number $l=2$ as an emergent property of the many-body system. Our interaction potential is attractive at a finite distance ${r}_{0},$ and the breaking of the rotational symmetry is the result of an interplay between ${r}_{0}$ and the interparticle distance ${r}_{s}.$ This interplay is generic to interactions of this type and is responsible for the existence of d-wave pairing for a range of densities. However, we find that $l=2$ pairing takes place only in the BCS limit. In contrast, as the Bose-Einstein (BE) limit is approached the internal energy of the ``preformed pairs'' becomes the dominant contribution and there is a quantum phase transition in which the s-wave symmetry is restored. We also find that the limiting value of the critical temperature is ${k}_{B}{T}_{c}\ensuremath{\rightarrow}3.315{\ensuremath{\Elzxh}}^{2}{/2m}^{*}[n/2(2l+1){]}^{2/3},$ which coincides with the usual result only for $l=0;$ for $l>0,$ it differs in the degeneracy factor $1/(2l+1),$ which lowers ${T}_{c}.$ Our results thus place constraints on exotic pairing in the BE limit, while at the same time indicating a particularly interesting route to pairing with $l>0$ in a BCS superconductor.

DOI
10.1103/physrevb.66.214526

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Superconductivity beyond the Gorkov decoupling is examined with an emphasis on the thermodynamic properties. In the Gorkov decoupling, the interaction term is factorized into the pairing correlation. Therefore, in contrast to the strong pair-pair correlation in coordinate space, the correlation between the Cooper pairs in momentum space is neglected. In this paper, in addition to the conventional pairing interaction, we consider a more general type of attractive interaction that cannot be factorized into the product of the pairing correlation. Accordingly, it becomes necessary to include the neglected correlation. We assume a variational functional where the general type of interaction is taken into account, and determine the state self-consistently at finite temperature. The following results are obtained: (1) The state obtained is more stable at low temperature, compared with the BCS state with the same parameters. (2) As the temperature is increased, our state approaches the BCS state. (3) At the same temperature as in the BCS theory, our system undergoes a phase transition from the superconducting phase to the normal phase.
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