Superconductivity as a Bose-Einstein condensation?

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique linear dispersion relation appropriate to weakly-coupled “bosonic” CPs moving in the Fermi sea—rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D. Corresponding author: M. de Llano [email protected] Bose-Einstein condensation (BEC) of Cooper pairs (CPs) leads to a phase transition even in 2D in any many-fermion system dynamically capable of forming CPs. This transition could be germane to superconductivity in the quasi-2D cuprates. In the weak coupling limit one finds a nearly linear dispersion relation for the CP that suggests very high, even diverging, critical temperatures Tc. On the other hand, in the strong coupling limit a nearly quadratic dispersion relation gives vanishingly small Tc’s. For intermediate coupling one gets the finite Tc’s appropriate for real quasi-2D superconductors. The single-Cooper pair problem may appear academic at first but has significant consequences. The familiar BEC formula for the transition temperature Tc ≃ 3.31h̄ n 2/3 B /mBkB , with nB the number density of bosons of mass mB and kB the Boltzmann constant, is a special case of the more general expression [1] valid for any space dimensionality d > 0 and any boson dispersion relation εK = CsK s with s > 0 and Cs a constant, given by