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

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.

5 pages, 2 figures

References in corpus (5)

• Role of the vortex-core energy on the Beresinkii-Kosterlitz-Thouless transition in thin films of NbN
• Superconducting phase transitions in ultrathin TiN films
• Size effects in the nonlinear resistance and flux creep in a virtual Berezinskii-Kosterlitz-Thouless state of superconducting films
• Influence of vortices and phase fluctuations on thermoelectric transport properties of superconductors in a magnetic field
• Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks

Cited by in corpus (5)

• Effective 2D thickness for the Berezinskii-Kosterlitz-Thouless-like transition in a highly underdoped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Substrate mediated nitridation of niobium into superconducting Nb2N thin films for phase slip study
• Suppression of the Berezinskii-Kosterlitz-Thouless and Quantum Phase Transitions in 2D Superconductors by Finite Size Effects
• Modeling and simulations of quantum phase slips in ultrathin superconducting wires
• Scaling of the magnetic permeability at the Berezinskii-Kosterlitz-Thouless transition from Coulomb gas simulations