Coherence length in superconductors from weak to strong coupling

Abstract

We study the evolution of the superconducting coherence length ${\xi }_0$ from weak to strong coupling, both within a s-wave and a d-wave lattice model. We show that the identification of ${\xi }_0$ with the Cooper-pair size ${\xi }_{pair}$ in the weak-coupling regime is meaningful only for a fully-gapped (e.g., s-wave) superconductor. Instead in the d-wave superconductor, where ${\xi }_{pair}$ diverges, we show that ${\xi }_0$ is properly defined as the characteristic length scale for the correlation function of the modulus of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between particle-particle and particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that ${\xi }_0$ is of order of the lattice spacing at finite densities. In the diluted regime ${\xi }_0$ diverges, recovering the behavior of the coherence length of a weakly interacting effective bosonic system. Similar results are expected to hold for d-wave superconductors.

11 pages, 5 figures. Two appendices and new references added

References in corpus (2)

• Discovery of microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x
• Phase fluctuations in superconductors: from Galilean invariant to quantum XY models

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