QUASI-PARTICLE BAND-STRUCTURE AND GAPLESS SUPERCONDUCTIVITY IN THE VORTEX-LATTICE STATE

The quasi-particle spectrum for s-wave superconductors in the Vortex-l attice state remains gapless in magnetic fields much below the upper c ritical field H-c2 where the cyclotron frequency is smaller than the a mplitude of the pair potential. This is shown through self-consistent solutions of the Bogoliubov-de Gennes equations for the attractive Hub bard model on the square lattice. It has not been predicted in earlier theoretical works based on a continuous model because it is due to th e dispersion of Landau subbands in the lattice model.