Abstract
After initial calculations for a single vortex, where the Bogoliubov-de Gennes equations, corresponding to a simple tight-binding model, are solved using the recursion method, a fully self-consistent microscopic solution for the Abrikosov flux lattice is given. In the case of the latter, the observation of discrete Landau-like levels with a large order parameter suggests a form for the energy spectrum which can give rise to oscillations of the thermodynamic potential as the magnetic field varies, even when there are no normal electrons in the system. These de Haas-van Alphen oscillations are studied analytically following a generalized version of the Lifshitz-Kosevich argument, and it is found that their amplitude in the superconducting state is damped compared with what they would have been in the normal state. These results are supported by further, approximate, computations.