electron systems are expected to exhibit strikingly new phenomena in the superconducting state when placed under strong quantising magnetic fields. We analyse the n~tute of the field dependent magnetization around the normai-superconducting phase boundary at low temperatures. Under ideal conditions (i.e. for sufficiently weak electron scattering by sideorder) both the normal and the superconducting components of the magnetlsation are in the 2D quantum diamagnetic regime, i.e. both are purely oscillatory and of the same order of magnitude. Unlike the normal 2D magnetooscillations, however, which are generated only by the two Landau levels adjacent to the Fermi energy, the superconducting ones involve many Landau levels around the Fermi energy and have a gapless structure. In contrast to the usual dHvA oscillations pattern, the amplltude of the oscillations' envelop is shown to increase with the decreasing field below Hc2(T), up to a ma;xS_mum located at lower fields for lower Temperatures.
Under the conditions of zero spin splitting the system may crossover into a new (reentrant) superconducting state, driven by the (resonant) pairing of many electrons within a single Landau level.