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 fields. 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 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.

Substrate mediated nitridation of niobium into superconducting Nb2N thin films for phase slip study

“…Generally, microscopic inhomogeneities 40 , disorder 41 , vortex-antivortex movement in 2D 23 , quantum fluctuation 4 , FSE particularly for the case of nanoscale granular systems 35,40,42,43 are the main reasons behind the rounding of the transition, deviation from the BKT model, resistive tailing and residual resistance at temperature T ≤ T c0 . Inhomogeneity and disorder play very crucial roles in the granular superconductors where disorder can cause a suppression of the PE coupling which establishes the superconductivity 19 .…”

Effective two-dimensional thickness for the Berezinskii-Kosterlitz-Thouless-like transition in a highly underdopedLa2−xSrxCuO4

“…Finally, we remark that, in our samples, we do not expect to observe the Ohmic response in the I − V char- acteristics caused by finite-size effects. [68][69][70][71] Indeed, it is known that the dc I − V curves probe the contribution of dissociated vortex-antivortex pairs separated by a distance r * = 2πJ s cW/Φ 0 I. Therefore, at small currents, which probe r * larger than the sample width (W < L), the free vortices will dominate the resistance and the I − V characteristics will be Ohmic.…”

Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects

“…It controls the density of free vortices n F which determines the sheet resistance (R ∝ n F ) as well as the correlation length (ξ ∝ n −1/2 F ) at and above T c . 24,25 Accordingly, the correlation length cannot grow beyond L. In this context it is important to recognize that the finite size scaling approach adopted here is compatible with the Harris criterion, 26,27 stating that short-range correlated and uncorrelated disorder is irrelevant at the BKT critical point, contrary to approaches where the smearing of BKT criticality is attributed to a Gaussian-like distribution of the bare superfluid-stiffness around a given mean value. 28 In this context it should be recognized that irrelevance of this disorder applies to the universal properties, while the nonuniversal parameters, including T c and the vortex core radius, may change.…”

“…The finite size effects stemming from the limited extent of the homogeneous domains or the applied magnetic field have a profound influence on the observation of the BKT behavior and have been studied intensely in recent years. 9,24,25,29,30 On the other hand, over the years, consistency with BKT behavior has been reported in thin films, 17,[29][30][31][32][33][34][35] and in systems exhibiting interfacial superconductivity. [7][8][9]24 Here we extend previous work 9,24,29,30 and analyze the sheet resistance data of Bi-films 6 and the LaAlO 3 /SrTiO 3 interface 8,9 using the finite size scaling formulas appropriate for the BKT transition, which include multiplicative corrections when present.…”