Quasiclassical theory of superconducting states under magnetic fields: Thermodynamic properties

TL;DR

This paper introduces a simplified quasiclassical approach to calculate thermodynamic properties of superconductors under magnetic fields, applicable to complex multiband and unconventional pairing states with minimal numerical effort.

Contribution

It develops an analytic scheme within quasiclassical theory for spatially-averaged thermodynamic properties of superconductors, including multiband and unconventional pairings, with broad applicability and reduced computational complexity.

Findings

Validated the theory against previous numerical studies.

Applied the method to s-wave, d-wave, and two-band s-wave pairings.

Demonstrated the approach's usefulness in analyzing experimental data.

Abstract

We present a simple calculational scheme for superconducting properties under magnetic fields. A combination of an approximate analytic solution with a free energy functional in the quasiclassical theory provides a wide use formalism for spatial-averaged thermodynamic properties, and requires a little numerical computation. The theory covers multiband superconductors with various set of singlet and unitary triplet pairings in the presence of an impurity scattering. It is also applicable to analyze experimental results in a rotating magnetic field with help of band structure calculations. We demonstrate the application to s-wave, d_{x^2-y^2}-wave and two-band s-wave pairings, and discuss the validity of the theory comparing with previous numerical studies.