Coherence lengths for three-dimensional superconductors in the BCS-Bose picture

R. M. Carter; M. Casas; J. M. Getino; M. de Llano; A. Puente; H. Rubio; D. M. van der Walt

doi:10.1103/PhysRevB.52.16149

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Coherence lengths for three-dimensional superconductors in the BCS-Bose picture

R. M. Carter, M. Casas, J. M. Getino, M. de Llano, A. Puente, H. Rubio, D. M. van der Walt

DOI 10.1103/PhysRevB.52.16149 · Physical Review B

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Abstract

Following an approach similar to that of Miyake or Randeria, Duan, and Shieh in two dimensions, we study a three-dimensional many-fermion gas at zero temperature interacting via some short-ranged two-body potential. To accommodate a possible singularity (e.g., the Coulomb repulsion) in the interaction, the potential is eliminated in favor of the two-body scattering t-matrix, the low-energy form of which is expressible in terms of the s-wave scattering length as. The BCS gap equation for s-wave pairing is then solved simultaneously with the number equation in order to self-consistently obtain the zero-temperature BCS gap Δ as well as the chemical potential μ as functions of the dimensionless coupling variable λ≡kFas, where kF is the Fermi momentum. Results are valid for arbitrary coupling strength, and in the weak coupling limit reproduce the standard BCS results. Finally, root-mean-square pair sizes are obtained as a function of λ and compared with experimental values.