De Haas-van Alphen effect in the superconducting state

Quantum oscillations were first observed in the mixed state of a superconductor, NbSe2, by Graebner and Robbins in 1976. More recently, the investigation of a number of other materials has shown that de Haas-van Aiphen effect oscillations persist below B-c2 in many systems, so that quantum oscillations in the vortex state appear to be the rule rather than the exception. Such measurements demonstrate that the effects of Landau quantization persist in the mixed state of a clean type II superconductor. In this paper we review work on NbSe2, V3Si and Nb3Sn, for which detailed measurements exist. We find that the principal effect of the superconducting order parameter is to reduce the amplitude of the oscillatory magnetisation. In principle, quantum oscillatory measurements of this type will give detailed information on the anisotropies of the superconducting state.