Self-Consistent Theory of Normal-to-Superconducting Transition

TL;DR

This paper develops a self-consistent Ginzburg-Landau theory for the normal-to-superconducting transition, demonstrating it is second-order and correcting previous beliefs of a fluctuation-driven first-order transition.

Contribution

It introduces a comprehensive analysis of the NS transition considering fluctuations for arbitrary dimensions and order parameter components, resolving prior inconsistencies and providing new critical exponent calculations.

Findings

Transition is second-order, not first-order as previously thought.

Calculated the anomalous exponent η(d,m) at the transition, approximately -0.38 in 3D for m=1.

The theory aligns with known expansions in certain limits and offers interpolation for general cases.

Abstract

I study the normal-to-superconducting (NS) transition within the Ginzburg-Landau (GL) model, taking into account the fluctuations in the $m$-component complex order parameter $\psi\a$ and the vector potential $\vec A$ in the arbitrary dimension $d$, for any $m$. I find that the transition is of second-order and that the previous conclusion of the fluctuation-driven first-order transition is an artifact of the breakdown of the $\eps$-expansion and the inaccuracy of the $1/m$-expansion for physical values $\eps=1$, $m=1$. I compute the anomalous $\eta(d,m)$ exponent at the NS transition, and find $\eta (3,1)\approx-0.38$. In the $m\to\infty$ limit, $\eta(d,m)$ becomes exact and agrees with the $1/m$-expansion. Near $d=4$ the theory is also in good agreement with the perturbative $\eps$-expansion results for $m>183$ and provides a sensible interpolation formula for arbitrary $d$ and $m$.