Superfluid characteristics of the attractive Hubbard model for various lattice structures

Abstract

We study the basic thermodynamic and electromagnetic properties of the superconductor described by the negative- U Hubbard model (gap parameter Δ, critical temperature T c, London penetration depth λ, thermodynamic critical field H c and Ginzburg-Landau correlation length ξ GL). The calculations are performed for square (SQ, d = 2), simple cubic (SC, d = 3) and face-centered cubic (FCC, d = 3) lattices. We analyze the results as a function of electron density n and interaction U using the Hartree-Fock approximation in the weak-to-intermediate U case combined with the conclusions from the perturbation theory valid in the strong coupling limit. From the equality: λ/ ξ GL = 1/√2 we find the boundaries between local and nonlocal electronic behaviour of the U < 0 Hubbard model in the U- n parameter space. Using the calculated values of T c and λ we compare the “universal plot” of T c/ T c m versus [ λ(0)/ λ m(0)] 2 (where: T c m denotes maximum T c as a function of n and λ m(0) corresponds to T c m) with the recent experimental data for various families of nonconventional superconductors and conclude that the best agreement can be obtained for intermediate values of the local attraction.