Strong quantum oscillations in the order parameter of two-dimensional type-II superconductors

Strong magnetic quantum oscillations in the order parameter are predicted to appear at low temperatures in extremely type-II, highly two-dimensional superconductors. The mean-square modulus of the order parameter over the entire vortex lattice near ${\mathit{H}}_{\mathit{c}2}$(T) is calculated using the Gorkov’s scheme in the semiclassical approximation. It is found that the strong magnetic quantum oscillations in the order parameter may yield a periodic reentrance of the superconducting state in the vicinity of the upper critical field, smearing greatly the superconducting transition. In systems with critical fields as high as those in the high-${\mathit{T}}_{\mathit{c}}$ cuprates, the fine structure of the oscillations is affected by the pairing correlation. The experimental feasibility of observing quantum oscillations in the highly two-dimensional, high-${\mathit{T}}_{\mathit{c}}$ bismuth compounds is discussed. They are found to persist well below ${\mathit{H}}_{\mathit{c}2}$(T), indicating the possibility of observing quantum oscillations in the order parameter at experimentally accessible fields.