Monte Carlo calculation of the current-voltage characteristi(12)

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

IV.MONTECARLOSIMULATION

Inthissectionwedescribehowwecalculatecurrent-voltagecharacteristicsbyMonte

CarlosimulationofthelatticeCoulombgas.

ThealgorithmtosimulatethelatticeCoulombgasworksasfollows[15]:Firstwepick

anearest-neighborpair(i,j)oflatticesitesatrandom.Thenwetrytoincreasenibyone

andtodecreasenjbyone,thuspreservingoverallvortexneutrality, ini=0.ThisMonte

Carlomoveofinsertinganeutralpairwillbeinterpretedastransferofoneunitvortexfrom

sitejtoi.Iftheenergychangeis Eweacceptthistrialmoveaccordingtothestandard

Metropolisalgorithm[22]withprobabilityexp( E/T).ThesesimpleMonteCarlomoves

canbothcreate,annihilate,andmovevortices.Thermodynamicaveragesarecomputedas

MonteCarlotimeaveragesoverthesequenceofgeneratedcon gurations.

TocalculateIVcharacteristicsworksasfollows[10,11]:Anappliedcurrentdensityj

givesaLorentzforceofjh/(2e)onaunitvortex.TheLorentzforcecanbeincorporatedin

theMonteCarlomoves[10]byaddingto Eanextratermjh/(2e)iftheunitvortexmoves

inthedirectionoppositetotheLorentzforce,subtractingthistermifitmovesinthesame

direction,andmakingnochangein Eifitmovesinaperpendiculardirection.Biasingthe

MonteCarlomovesinthiswaytakesthesystemoutofequilibriumandcausesanet uxof

vorticesinadirectionperpendiculartothecurrent.Thisgeneratesavoltagegivenbythe

Josephsonrelation:

V=h