Parquet Graph Resummation Method for Vortex Liquids

TL;DR

This paper introduces a nonperturbative parquet graph resummation method for vortex liquids in superconductors, deriving integral equations to analyze structure factors and translational order in 2D and 3D systems, including disorder effects.

Contribution

The paper develops a novel nonperturbative approach using parquet graph resummation for vortex liquids, providing integral equations and numerical solutions for structure factors and order parameters.

Findings

Growing translational order with decreasing temperature in 2D vortex liquids

Disorder causes a smooth decrease in the correlation length $R_c$

Numerical solutions reveal temperature dependence of order in pure and disordered systems

Abstract

We present in detail a nonperturbative method for vortex liquid systems. This method is based on the resummation of an infinite subset of Feynman diagrams, the so-called parquet graphs, contributing to the four-point vertex function of the Ginzburg-Landau model for a superconductor in a magnetic field. We derive a set of coupled integral equations, the parquet equations, governing the structure factor of the two-dimensional vortex liquid system with and without random impurities and the three-dimensional system in the absence of disorder. For the pure two-dimensional system, we simplify the parquet equations considerably and obtain one simple equation for the structure factor. In two dimensions, we solve the parquet equations numerically and find growing translational order characterized by a length scale $R_c$ as the temperature is lowered. The temperature dependence of $R_c$ is obtained in both pure and weakly disordered cases. The effect of disorder appears as a smooth decrease of $R_c$ as the strength of disorder increases.