Monte Carlo calculation of the current-voltage characteristi(15)

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

lengthequalsthesystemsize,andthenonlineardependenceoftheresistanceonthecurrent

vanishes.Theregimewhereweprobethenon-linearIVcharacteristicisforthis gure

approximatelyfromlnj≈ 1.5upto≈ 0.5.AccordingtotheKosterlitz-Thoulesstheory

theslopeofthelinesshouldbe3atthecriticaltemperature,andthiscriteriacanbeusedto

determineTc.Wewillhoweveruseanindependentdetermination[12]ofTcforthissystem,basedonthe nitesizescalingrelationEq.(6).

InFig.1bwedemonstratethee ectsofthe nitelatticesizeforlowdrivingcurrents

attemperaturesbelowTc.ThedatashownareforT=0.15andlatticesizesareL=8

(triangles),12(opensquares),16(stars),24(opencircles),and32( lledcircles).

The nitesizee ectsforthelowertemperaturescanbeunderstoodinthefollowingway.

(SeethediscussionabovefollowingEq.(15).)The nitelatticesizeisimportantbecause

pairexcitationoverthebarriergivenbytheperiodicitylengthLwilladdtothedissipation

duetounbindingofpairsoverthebarriergivenbythepairsizer .Theinducedelectric

eldwillaccordinglybeoftheform

E=R(L)j+constantjE1/2T+1,(26)

wherethe rsttermR(L)followsfromEq.(16)andR(L)→0asL→∞.Thesecond

terminEq.(26)isgivenbyEq.(15)andwillremain niteinthelimitL→∞.Thisis

clearlydemonstratedinFig.1bwhereweseethatthecrossoverinEq.(26)betweenthe

linearandnonlinearregimeappearsatahigherdrivingcurrentforthesmaller8×8lattice

asthecurrentlength(E1/I=ξI～L)associatedwiththecurrentdensityjexceedsthesize

ofthelattice.

InFig.2theexponentaIV(X)isshownasafunctionofthereducedtemperature

X=T/Tc.ThedashedhorizontallinerepresentstheuniversaljumpconditionforaIV(X).

TheplussesrepresentexperimentaldatafromasuperconductingHg-Xe lm[4,26].The

lledcirclesaretheresultsforaIV(T)fromFig.1.Theotherthreedatasetsarefor

latticesizesL=16(stars),24(opencircles),and48(triangles).Asonecanseethereare

noapparent nitesizee ectsinthedata.Inthevicinityofthecriticaltemperaturethe