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 {ital et} {ital al}. (Phys. Rev. Lett. 64, 966 (1990)). When the magnetic field {bold B} and the current density {bold J} make an angle {phi}, the resistivity at sufficiently high temperatures roughly obeys the law {rho}({ital B},{ital T},{phi})={rho}{sub 0}({ital B},{ital T})+{Delta}{rho} sin{sup 2}({phi}) in agreement with experiment. The resistivity is strongly dependent on current density. At zero magnetic field it is found to satisfy the scaling relation {ital E}={xi}{sup {minus}1{minus}{ital z}F}{sub {plus minus}}({ital J}{xi}{sup {ital d}{minus}1}{Phi}{sub 0}/{ital ck}{sub {ital B}T}), where {ital E} is the electric field, {ital c} is the speed of light, {ital J} is the current density, {ital d} is the dimensionality, and {ital F}{sub {plus minus}} are scaling functions which apply above and below {ital T}{sub {ital c}}. The dynamical critical exponent is estimated for this model as 1.5{plus minus}0.5.