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

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

2012-03-23

arxiv.org/abs/1203.5317v1

Physics

Condensed Matter

Superconductivity

Scientific paper

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 $T_c$, 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 $T_c$, all 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.

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