Scaling, Finite Size Effects, and Crossovers of the Resistivity and Current-Voltage Characteristics in Two-Dimensional Superconductors

TL;DR

This paper analyzes the scaling behavior of resistivity and current-voltage characteristics in 2D superconductors near the BKT transition, revealing crossover effects, logarithmic corrections, and clarifying experimental-simulation discrepancies.

Contribution

It introduces a detailed renormalization group analysis of finite size effects and crossovers, including the impact of vortex fugacity and magnetic field, with numerical validation.

Findings

Logarithmic corrections significantly affect scaling near Tc.

Approaching the transition in a magnetic field simplifies the scaling analysis.

Numerical simulations confirm the theoretical predictions and determine the dynamic critical exponent z.

Abstract

We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below Tc, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field, or system size is varied, and find a strong multiplicative logarithmic correction near Tc, all of which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large-scale numerical simulations, and calculate the dynamic critical exponent z, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.