Reentrant superconductivity in a strong applied field within the tight-binding model

It was suggested by Rasolt and Te\v{s}anovi\'c that the Landau level quantization in isotropic superconductors could enhance superconductivity in a very strong magnetic field, above the upper critical field ($H_{c2}$). We derive a generalized Harper equation for superconducting systems, and show that a similar reentrant behavior appears in a lattice model, even though the Landau--level--structure is destroyed by the periodic potential in that case. Both the orbital and the Zeeman field--induced effects are taken into account.