Extreme Type-II Superconductors in a Magnetic Field: A Theory of Critical Fluctuations

TL;DR

This paper develops a novel theoretical framework for understanding critical fluctuations in extreme type-II superconductors under weak magnetic fields, linking gauge theory concepts to vortex behavior and critical phenomena.

Contribution

It introduces a new mapping of the Ginzburg-Landau problem to a gauge theory with zero effective magnetic field, providing insights into vortex fluctuations and critical behavior in high-temperature superconductors.

Findings

Relation to anisotropic gauge theory with 'charge' role of magnetic field

Insights into vortex line liquid and normal state nature

Proposed minimal requirements for vortex-lattice melting theory

Abstract

A theory of critical fluctuations in extreme type-II superconductors subjected to a finite but weak external magnetic field is presented. It is shown that the standard Ginzburg-Landau representation of this problem can be recast, with help of a novel mapping, as a theory of a new "superconductor", in an effective magnetic field whose overall value is zero, consisting of the original uniform field and a set of neutralizing unit fluxes attached to $N_{\Phi}$ fluctuating vortex lines. The long distance behavior is related to the anisotropic gauge theory in which the original magnetic field plays the role of "charge". The consequences of this "gauge theory" scenario for the critical behavior in high temperature superconductors are explored in detail, with particular emphasis on questions of 3D XY vs. Landau level scaling, physical nature of the vortex "line liquid" and the true normal state, and fluctuation thermodynamics and transport. A "minimal" set of requirements for the theory of vortex-lattice melting in the critical region is also proposed and discussed.