Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within the Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of perturbation theory to fourth and eight order against an exact numerical solution of the corresppnding Bogolubov-de Gennes equations.The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_c2$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA- oscillations below $H_c2$. Instead we obtain a substantional damping of the magnetic oscillations in the mixed state as compared to the normal state. The temperature and spin dependence of the oscillations in the mixed state is found to be the same as in the normal state. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. We conclude that both within perturbation theory and the exact solution there is no such effect.