The Ginzburg-Landau Theory of Type II superconductors in magnetic field

TL;DR

This paper develops a comprehensive Ginzburg-Landau theoretical framework for understanding the thermodynamics, vortex phases, and effects of thermal fluctuations and disorder in type II superconductors under magnetic fields, with experimental comparisons.

Contribution

It introduces systematic analytical methods for vortex matter phases, including flux lattice, vortex liquid, and vortex glass, and extends the theory to high-temperature superconductors and other physical systems.

Findings

Derivation of Abrikosov flux lattice solution with systematic improvements.

Quantitative theory of vortex melting line and liquid state characteristics.

Analysis of vortex glass properties using the replica method.

Abstract

Thermodynamics of type II superconductors in electromagnetic field based on the Ginzburg - Landau theory is presented. The Abrikosov flux lattice solution is derived using an expansion in a parameter characterizing the "distance" to the superconductor - normal phase transition line. The expansion allows a systematic improvement of the solution. The phase diagram of the vortex matter in magnetic field is determined in detail. In the presence of significant thermal fluctuations on the mesoscopic scale (for example in high $T_{c}$ materials) the vortex crystal melts into a vortex liquid. A quantitative theory of thermal fluctuations using the lowest Landau level approximation is given. It allows to determine the melting line and discontinuities at melt, as well as important characteristics of the vortex liquid state. In the presence of quenched disorder (pinning) the vortex matter acquires certain "glassy" properties. The irreversibility line and static properties of the vortex glass state are studied using the "replica" method. Most of the analytical methods are introduced and presented in some detail. Various quantitative and qualitative features are compared to experiments in type II superconductors, although the use of a rather universal Ginzburg - Landau theory is not restricted to superconductivity and can be applied with certain adjustments to other physical systems, for example rotating Bose - Einstein condensate.