Superfluid characteristics of the attractive Hubbard model for various lattice structures

We study the basic thermodynamic and electromagnetic properties of the superconductor described by the negative-$U$ Hubbard model (gap parameter $\Delta$, critical temperature $T_c$, London penetration depth $\lambda$, thermodynamic critical field $H_c$ and Ginzburg-Landau correlation length $\xi_{G-L}$).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: $\lambda/\xi_{G-L}}=1/\sqrt{2}$ 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 $\lambda$ we compare the `universal plot' of $T_c/T_c^m$ vs. $[\lambda(0)/\lambda^m(0)]^2$ ( where: $T_c^m$ denotes maximum $T_c$ as a function of $n$ and $\lambda^m(0)$ 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. Keywords: negative-$U$ Hubbard model, London penetration depth, high-$T_c$ superconductivity