H. Rubio

Cooper pairing in the van hove singularity scenario of high-temperature superconductivity

Abstract Cooper pairing is shown to exist, and to be much stronger, when a density of states with a van Hove singularity is used in place of the usual smooth one. The binding energy for weak coupling again has an essential singularity but in the square root of the coupling constant, a property surviving in the BCS gap energy expression obtained by other workers.

Cooper pairing in one, two, and three dimensions

The Cooper pair eigenvalue equation is solved exactly for the free‐electron density of states in one, two, and three dimensions. The two‐dimensional (2‐D) case is essentially the original derivation of Cooper, as is the three‐dimensional case if the interaction is restricted to the vicinity of the Fermi surface. The essential singularity in coupling, familiar in 2‐D quantum binding in a well, and sometimes erroneously attributed to the two‐dimensional character of the BCS model interaction which is nonzero only very near the Fermi surface, appears in all three cases.

BCS-bose theory of the superconducting coherence length

Abstract A root-mean square fermion pair radius, defined in terms of an appropriate BCS-Bose pair wave function in momentum space, is obtained analytically in one- and three-dimensions via complex plane integration. Results are compared with the familiar Pippard coherence length, in weak coupling (BCS regime), and with the size of an isolated pair in strong coupling (Bose regime). Inspite of their comparatively small magnitudes, empirical cuprate coherence length data seem to be consistent with a weakly-coupled description within the BCS-Bose picture.