Gauge-invariant theory of the Meissner effect in the lattice model of a superconductor with local pairing

T. Kostyrko; R. Micnas; K. A. Chao

doi:10.1103/PhysRevB.49.6158

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Gauge-invariant theory of the Meissner effect in the lattice model of a superconductor with local pairing

T. Kostyrko, R. Micnas, K. A. Chao

DOI 10.1103/PhysRevB.49.6158 · Physical Review B

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Abstract

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 condition of the gauge invariance to the case of the tight-binding model of the 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 part of the response kernel is modified by the collective effects, contrary to the continuum model. We find that the response kernel shows substantial anisotropy in the long-wavelength limit in both weak- and strong-coupling regimes. With the numerical results for the square lattice, we examine evolution of the kernel with the change of the coupling strength and band filling.