Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors

TL;DR

This paper derives a generalized Ginzburg-Landau functional to describe the FFLO superconducting state near the tricritical point across different dimensions, revealing the nature of phase transitions and providing a basis for numerical analysis.

Contribution

It introduces a generalized GL functional for FFLO states in 1, 2, and 3 dimensions, detailing transition orders and state transformations.

Findings

Second order transition in 1D and 2D

First order transition in 3D

Sine modulation transforms into soliton-lattice in 1D

Abstract

We derive a generalized Ginzburg-Landau (GL) functional near the tricritical point in the (T,H)-phase diagram for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state, in 1,2, and 3 dimensions. We find that the transition from the normal to the FFLO state is of second order in 1 and 2 dimensions, and the order parameter with one-coordinate sine modulation corresponds to the lowest energy near the transition line. We also describe in the one-dimensional case the transformation of the sine modulation into the soliton-lattice state as the magnetic field decreases. In 3 dimensions however, we find that the transition into an FFLO state is of first order, and it is impossible to obtain an analytic expression for the critical temperature. In this case the generalized GL functional proposed here provides a suitable basis for a numerical study of the properties of the FFLO state, and in particular for computing the critical temperature, and for describing the transition into a uniform state.