Interplay of paramagnetic, orbital and impurity effects on the phase transition of a normal metal to superconducting state

TL;DR

This paper derives a generalized Ginzburg-Landau theory to analyze how paramagnetic, orbital, and impurity effects influence the phase transition to superconductivity, revealing the conditions for non-uniform states and phase diagram sensitivities.

Contribution

It introduces a comprehensive free energy functional accounting for multiple effects and provides phase diagrams for different superconductor types and geometries, including instability criteria.

Findings

Superconducting phase diagram is highly sensitive to geometry and order parameter.

Conditions for non-uniform (Fulde-Ferrell-Larkin-Ovchinnikov) states are established.

Instability criteria for non-uniform states in dirty s-wave superconductors are derived.

Abstract

We derive the generalized Ginzburg-Landau free energy functional for conventional and unconventional singlet superconductors in the presence of paramagnetic, orbital and impurity effects. Within the mean field theory, we determine the criterion for appearence of the non uniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state, with vortex lattice structure and additional modulation along the magnetic field. We also discuss the possible change of the order of transition from normal to superconducting state. We find that the superconducting phase diagram is very sensitive to geometrical effects such as the nature of the order parameter and the shape of the Fermi surface. In particular, we obtain the qualitative phase diagrams for three-dimensional isotropic s-wave superconductors and in quasi two-dimensional d-wave superconductors under magnetic field perpendicular to the conducting layers. In addition, we determine the criterion for instability toward non uniform superconducting state in s-wave superconductors in the dirty limit.