Theory of the Amplitude of the de Haas-van Alphen Oscillation in the Superconducting Mixed State: Effects of the Eddy Currents

The amplitude of the de Haas-van Alphen (dHvA) oscillation in the superconducting mixed state, which is measured by the field modulation method, is calculated. We investigate the effects of the superconducting eddy currents on the voltage signal from a pick-up coil, assuming that a finite conductivity, which may originate from the flux flow for example, exists in the mixed state. In a material which has a small Fermi surface, the Shubnikov-de Haas (SdH) effect contributes to the voltage signal in addition to the dHvA effect; therefore the amplitude of the voltage becomes larger than that of only the dHvA effect. In a material which has a large Fermi surface, the amplitude is hardly affected by the SdH effect and becomes smaller due to the skin effect. The present results have the same tendency with the experimental data of NbSe₂ as an example of a small Fermi surface and V₃Si as an example of a large Fermi surface.