Self-Consistent Theory of Normal-to-Superconducting Transition

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 $ψ\a$ 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 $m$.

9 pages, TeX + harvmac.tex (included), 2 figures and hard copies are available from [email protected] To appear in Europhysics Letters, January, 1995

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