Monte Carlo calculation of the current-voltage characteristi(5)

We have studied the nonlinear current-voltage characteristic of a two dimensional lattice Coulomb gas by Monte Carlo simulation. We present three different determinations of the power-law exponent $a(T)$ of the nonlinear current-voltage characteristic, $V

gastemperature[3].Thetraceisoverni=0,±1onallsitesi,subjecttooverallneutrality,

ini=0.GijisthelatticeGreen’sfunctionforthelogarithmic2Dvortexinteraction,

Gij=1

2 cos(kx) cos(ky),(4)

wherekarethereciprocallatticevectors,kx,ky=2πn/L,n=0,...,L 1.

WewillcalculatetheresponsevoltagetoanappliedcurrentimposedontheCoulomb

gas.Theabovede nitiondoesnotincludeanynetcurrents.Howtoincludethemandto

calculateIVcharacteristicsbyMonteCarlosimulationisdescribedinthenextsection.

III.CURRENT-VOLTAGECHARACTERISTICS

Inthissectionwediscussvariousaspectsandapproachestothecurrent-voltagecharac-

teristicsof2DsuperconductorsclosetotheKosterlitz-Thoulesstransition.

A.Linearresistance

Abasicexperimentonasuperconductoristomeasurethelinearresistance.Suchmea-

surementsonthin lmsofbothconventionallow-Tcsuperconductors[4]andsinglecrystal

high-Tcmaterials[7,8],havebeensuccessfullyinterpretedintermsofthermallyexcited

vortex uctuationsanalyzedbyuseoftheCoulombgas[3].

Thelinearresistivityisde nedbyρ=E/jforj→0,wherejistheappliedsupercurrent

densityandEistheresultinginducedelectric eld.Somewordsaboutnotation:Since

resistanceandresistivityhavethesamedimensionintwodimensionsandoursystemis

homogeneous,theyarethesame,andtheywewillbothbedenotedbyR.Rwillbe

reservedforlinearresistance,andwillnotbeusedtodenotenonlinearresistance.An

appliedsupercurrentisdenotedbyI=jL,andvoltageisV=EL.

TodeterminethelinearresistanceinsimulationsoftheCoulombgasfromE/jforsmall

jhasitslimitations,aswehavetorepeatthecalculationatasequenceofcurrentdensities

j,tomakesurethatjissmallenoughtobeinthelinearregime.Ifthepurposeisto