GAUGE-INVARIANT THEORY OF THE MEISSNER EFFECT IN THE LATTICE MODEL OFA SUPERCONDUCTOR WITH LOCAL PAIRING

We study a gauge-invariant theory of the response of a superconductor to the static magnetic field using the negative-U Hubbard Hamiltonian and the random phase approximation (RPA). We extend the usual conditio n of the gauge invariance to the case of the tight-binding model of th e superconductor and find it to be fulfilled by our RPA theory for all wave vectors in the Brillouin zone. At the same time the transverse p art of the response kernel s modified by the collective effects, contr ary to the continuum model. We find that the response kernel shows sub stantial anisotropy in the long-wavelength limit in both weak-and stro ng-coupling regimes. With the numerical results for the square lattice , we examine evolution of the kernel with the change of the coupling s trength and band filling.