Critical fluctuations in superconductors and the magnetic field penetration depth

TL;DR

This paper investigates the critical behavior of superconductors near the transition point using renormalization group methods, revealing a nonclassical penetration depth exponent and the relationship between magnetic penetration depth and correlation length.

Contribution

It provides a detailed analysis of critical fluctuations in superconductors, identifying a tricritical point and calculating critical exponents within a fixed-dimension RG framework.

Findings

Discovery of tricritical behavior in superconductors.

Identification of an attractive charged fixed point for certain parameters.

Determination that the magnetic penetration depth exponent is nonclassical.

Abstract

The superconducting transition is studied within the one-loop renormalization group in fixed dimension $D=3$ and at the critical point. A tricritical behavior is found, and for $\kappa > \kappa_c$, an attractive charged fixed point, distinct from that of a neutral superfluid. The critical exponents of the continuous transition are evaluated, and it is shown that the anomalous dimension of the gauge field equals unity. This implies the proportionality of the magnetic field penetration depth and the superconducting correlation length below the transition. The penetration depth exponent is nonclassical. We argue that it can not be extracted from the dual theory in a straightforward manner since it is not renormalized by fluctuations of the dual field.