Finite-Element and Effective-Medium Calculations of the Electrical Behaviour Near the Vortex–Antivortex Binding Transition of Planar Superconductors with Critical Temperature Inhomogeneities

We present calculations of the electrical behaviour near the Berezinskii–Kosterlitz–Thouless (BKT) vortex–antivortex binding transition of planar type- II superconductors with critical temperatures varying in space according to a random Gaussian distribution. By using a finite-element mesh-circuit analysis we obtain as a function of temperature and intensity the spatial maps of local voltages. These calculations allow us to argument that in these inhomogeneous superconductors the occurrence of a global voltage-current curve V ∝ I 3 signals with good accuracy the average BKT temperature because of the appearance of percolation-like configurations when 50 % of the sample has experienced the vortex–antivortex binding transition. In addition, we also present an effective-medium calculation aimed to obtain the resistance V / I without any finite-element computation. It leads to results in agreement with the finite-element approach except in the close vicinity of . For instance, for the upper part of the transition both theoretical approaches coincide in all the ohmic region of temperatures, including also the average mean-field temperature .