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

It was suggested by Rasolt and Tešanović [Rev. Mod. Phys. 64, 709 (1992)] that the Landau level quantization in isotropic superconductors could enhance superconductivity in a very strong magnetic field, above the upper critical field ${(H}_{c2\mathrm{}}).\mathrm{}$ 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.