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

TL;DR

This paper develops an exact analytical Ginzburg-Landau theory for strongly type-II superconductors at high magnetic fields, revealing non-local quantum oscillation effects linked to electron cyclotron motions and vortex lattice interactions.

Contribution

It introduces a new Green's function approach yielding an exact expression for the quartic term, highlighting singular non-local contributions and quantum oscillations in the superconducting free energy.

Findings

Reveals singular non-local contributions to free energy from cyclotron motions.

Shows vortex lattice disorder suppresses oscillatory quantum effects.

Identifies large paramagnetic-diamagnetic oscillations at low temperatures.

Abstract

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.