THE ANALOG OF THE LIFSHITZ-KOSEVICH FORMULA FOR THE DHVA EFFECT IN THE VORTEX STATE OF A 2-DIMENSIONAL SUPERCONDUCTOR

We study the effects of the superconducting (SC) order parameter on the magnetization oscillations in the vortex state of extremely type-II, nearly 2D superconductors. A systematic expansion of the electronic free energy in the SC order parameter, up to fourth order, is used to calcuate the magnetization oscillations just below H-c2(T). An analytical expression for the magnetization oscillations is derived. The resulting expression is a generalization of the well known Lifshitz-Kosevich formula, which is operative above H-c2, into the vortex state below H-c2. The expansion parameter clearly reflects the gapless nature of the quasi-particle spectrum below H-c2. The development of the SC order parameter with the decreasing magnetic field below H-c2 generates a significant contribution tot he magnetization oscillations in antiphase to the normal electrons oscillations. This seems to account for the significant reduction in the dHvA amplitude observed already in several superconductors just below H-c2.