Monte Carlo calculation of the current-voltage characteristi(2)

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

I.INTRODUCTION

Intwodimensionsthesuperconductingtransitioninzeromagnetic eldisaKosterlitz-

Thoulesstransition.[1–3]Thishasbeenveri edovertheyearsinbothexperiments[4]andin

manymodelsofsuperconductorsliketheXY,Villain,andCoulombgasmodels[1,5,6].The

importantdegreesoffreedominasystemundergoingaKosterlitz-Thoulesstransitionare

thermallyexcitedvortexpairs.TheKosterlitz-Thoulesstransitionissometimesalsoreferred

toasavortexunbindingtransition,asfortemperaturesbelowthetransitiontemperature

Tcallvorticesareboundinneutralpairs.ThesepairsstarttounbindatandaboveTc.

AtypicalwaytolookforaKosterlitz-Thoulesstransitioninexperimentsonthinsu-

perconducting lmsistoprobethecurrent-voltage(IV)characteristic[4,7,8].Boththe

linearandthenonlinearIVcharacteristicshavespeci c ngerprintsidentifyingaKosterlitz-

Thoulesstransition.VorticesdeterminetheIVcharacteristicforthefollowingreasons:If

avortexisdraggedacrossthesystemavoltageisinduced.Henceresistanceiszeroonlyif

therearenovorticesavailabletomoveacrossthesystem,andonlythenthesystemistruly

superconducting.Vorticesthatareboundinneutralpairsareunabletomovefreelyandto

causedissipation.Howeveranexternalappliedin-planesupercurrentyieldsaperpendicular

Lorentzforceactinginoppositedirectiononvorticeswithdi erentvorticity.Thisgivesa

net uxofvorticesacrossthesystem,whichshowsupasnonlinear(i.e.currentdependent)

resistance.

BelowtheKosterlitz-Thoulesstransitiontemperatureallvorticesareboundinneutral

pairsbythelogarithmicvortexinteraction,andthelinearresistanceisthuszero.Therefore

thesystemsuperconductsbelowtheKosterlitz-Thoulesstransition.Thelinearresistance

dropstozeroattheKosterlitz-Thoulesstransitionwithanexponentialfunctionalform,

R～ξ 2withlnξ～|T Tc| 1/2[3].Thisisconsistentwithexperiments,althoughthe

logarithmisacomplicationforquantitativecomparisonbetweentheoryandexperiment.A

niteappliedcurrentgivesapower-lawnonlinearIVcharacteristicoftheformV～Ia(T)+1.

Thecriticalcurrentisthuszero.AttheKosterlitz-ThoulesstransitiontheIVexponenta(T)