Monte Carlo calculation of the current-voltage characteristi(9)

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

TheenergyE(r)inEq.(8)hasa

maximumatseparationr =E1/Iandtheenergy

neededtoseparateavortexpairtothisdistanceis[4]:

E=E(r ) E(r=1)=E1ln(r ) I(r 1)

E=E1ln(E1(11)

nF.

AssumingthatΓisdeterminedbyactivationoverthebarrier Ewegetthefollowing

productionrate[17]

Γ∝e E

2T∝

∝

2Te 1I) E1+I) E12TeE1

keepingtheimportanttermforsmallbut niteIwearriveat:

R∝ E12T(15)

AgivencurrentIgivesrisetoa“currentlengthscale”r fromthemaximumconditionin

Eq.(8).Asthelatticeofthesystemhasa nitesize,thissetsanupperlimittothe“current

length”andhencealowerlimittothecurrentproducingnonlinearresistance.Thesmallest

currentgivingnonlinearresistanceisI =E1/r withr =Landhenceforcurrentssmaller