Flux-flow resistivity in model high-temperature superconductors

Abstract

We calculate the resistivity of a model ‘‘high-temperature superconductor’’ consisting of a simple-cubic arrangement of superconducting ‘‘grains’’ coupled together by resistively shunted Josephson junctions. The effects of temperature are simulated by Langevin noise in each junction. We find a strong magnetoresistance for magnetic fields both parallel and perpendicular to the applied current, in agreement with the results of Kwok et al. [Phys. Rev. Lett. 64, 966 (1990)]. When the magnetic field B and the current density J make an angle φ, the resistivity at sufficiently high temperatures roughly obeys the law ρ(B,T,φ)=ρ0(B,T)+Δρ sin2(φ) in agreement with experiment. The resistivity is strongly dependent on current density. At zero magnetic field it is found to satisfy the scaling relation E=ξ−1−zF±(Jξd−1Φ0/ckBT), where E is the electric field, c is the speed of light, J is the current density, d is the dimensionality, and F± are scaling functions which apply above and below Tc. The dynamical critical exponent is estimated for this model as 1.5±0.5.

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