Quantum oscillation in vortex states of type-II superconductors

We examine theoretically magnetic quantum oscillations like the de Haas–van Alphen and Subnikov–de Haas effects in vortex states in type-II superconductors. For a magnetic field B not very small compared with ${\mathit{H}}_{\mathit{c}3}$(T), the main effect of superconductivity is introduction of the extra quasiparticle scattering rate proportional to ‖Δ${\mathrm{\Vert }}^2$, the square of the superconducting order parameter. Therefore the detectability of the magnetic quantum oscillation is determined from the condition that the extra Dingle temperature due to ‖Δ${\mathrm{\Vert }}^2$ is not too large. For example in a magnetic field ∼10 T, the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ has to be less than 30 K in order to have a reasonable signal.