Theory of a Continuous H$_{c2}$ Normal-to-Superconducting Transition

TL;DR

This paper analyzes the $H_{c2}$ transition in the Ginzburg-Landau model, revealing a possible second-order transition in contrast to previous beliefs, and discusses the effects of thermal fluctuations and dimensionality on the transition nature.

Contribution

It provides an exact fixed point analysis in the large component limit, challenging the prior assumption of a first-order transition for the $H_{c2}$ transition.

Findings

Suggests a second-order transition in the large-m limit.

Identifies a lower critical dimension $d_{lc}=4$ for ODLRO survival.

Shows thermal fluctuations prevent ODLRO in 2D and 3D.

Abstract

I study the $H_{c2}$ transition within the Ginzburg-Landau model, with $m$-component order parameter $\psi_i$. I find a renormalized fixed point free energy, exact in $m\rightarrow\infty$ limit, suggestive of a $2$nd-order transition in contrast to a general belief of a $1$st-order transition. The thermal fluctuations for $H\neq 0$ force one to consider an infinite set of marginally relevant operators for $d<d_{uc}=6$. I find $d_{lc}=4$, predicting that the ODLRO does not survive thermal fluctuations in $d=2,3$. The result is a solution to a critical fixed point that was found to be inaccessible within $\epsilon=6-d$-expansion, previously considered in E.Brezin, D.R.Nelson, A.Thiaville, Phys.Rev.B {\bf 31}, 7124 (1985), and was interpreted as a $1$st-order transition.