Dual description of the superconducting phase transition

TL;DR

This paper reviews a dual theoretical framework for superconducting phase transitions, describing magnetic vortices and their role in the transition, and applies renormalization group theory to analyze critical behavior.

Contribution

It introduces a dual description of superconductivity involving vortex loops and analyzes the phase transition using renormalization group methods.

Findings

Vortex proliferation signals the transition from superconducting to normal phase.

The critical exponents match those of a superfluid with reversed temperature axis.

The dual theory captures the disorder field development in the normal phase.

Abstract

The dual approach to the Ginzburg-Landau theory of a Bardeen-Cooper-Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non-zero expectation value in the normal conducting phase. It thereby breaks a {\it global} U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting-to-normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second-order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.