Effects of critical temperature inhomogeneities on the voltage–current characteristics of aplanar superconductor near the Berezinskii–Kosterlitz–Thouless transition

Abstract

We analyze numerically how the voltage–current (V –I) characteristics near the so-called Berezinskii–Kosterlitz–Thouless (BKT) transition of 2Dsuperconductors are affected by a Gaussian distribution of critical temperatureinhomogeneities, randomly located in space and with long characteristic lengths (muchlarger than the in-plane superconducting coherence length amplitude). Our simulationsallow us to quantify the broadening around the average BKT transition temperature of both the exponent α in and of the resistance V/I. These calculations reveal that strong spatial redistributionsof the local current will occur around the transition as eitherI or thetemperature T are varied. Our results also support that the conditionα = 3 provides a good estimate for the location of the average BKT transition temperature, and that extrapolating to the α(T) behavior well below the transition provides a good estimate for the average mean-fieldcritical temperature .