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Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs

J. Batle·M. Casas M. Fortes·M. A. Solís·M. de Llano·A. A. Valladares·O. Rojo
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Abstract

Cooper pair (CP) binding with both zero and nonzero center-of-mass momenta (CMM) is studied with a set of renormalized equations assuming a short-ranged (attractive) pairwise interfermion interaction. Expanding the associated dispersion relation in 2D in powers of the CMM, in weak-to-moderate coupling a term {\it linear} in the CMM dominates the pair excitation energy, while the quadratic behavior usually assumed in Bose-Einstein (BE)-condensation studies prevails for any coupling {\it only} in the limit of zero Fermi velocity when the Fermi sea disappears, i.e., in vacuum. In 3D this same behavior is observed numerically. The linear term, moreover, exhibits CP breakup beyond a threshold CMM value which vanishes with coupling. This makes all the excited (nonzero-CMM) BE levels with preformed CPs collapse into a single ground level so that a BCS condensate (where only zero CMM CPs are usually allowed) appears in zero coupling to be a special case in either 2D or 3D of the BE condensate of linear-dispersion-relation CPs.

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J. Batle, M. Casas M. Fortes, M. A. Solís, M. de Llano, A. A. Valladares, O. Rojo. 2001-03-27. Bose-Einstein condensation of nonzero-center-of-mass-momentum Cooper pairs. https://doi.org/10.1016/s0921-4534(01)00745-6

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