Exact analytic Gorkov-Ginzburg-Landau theory of type-II superconductivity in the magneto-quantum oscillations limit

A new Green's function representation is employed in a microscopic derivation of a Ginzburg-Landau theory of strongly type superconductivity at high magnetic fields. An exact analytical, physically transparent expression for the quartic term in the corresponding order parameter expansion is presented. The resulting expression reveals singular non-local contributions to the superconducting (SC) free energy, associated with highly coherent cyclotron motions of the paired electrons near the Fermi surface, which are strongly coupled to the vortex lattice. A major part of these contributions arises from incoherent scattering by the spatially averaged pair-potential, which is purely harmonic in the de Haas van Alphen frequency. However, coherent scatterings by the ordered vortex lattice generate, at low temperatures, large erratically oscillating (i.e. paramagnetic-diamagnetic) contribution to the SC free energy as a function of the magnetic field. Vortex lattice disorder, which tends to suppress this oscillatory component, is found to preserve the singular harmonic part of the SC free energy.