Ajay Kumar GhoshJadavpur University

Kolkata, India

Vortex Line Ordering in the Driven 3-D Vortex Glass

Vortex Wrocław 2006

Stephen TeitelUniversity of Rochester

Rochester, NY USA

Peter OlssonUmeå University

Umeå, Sweden

uniform drivingforce

3D Frustrated XY Model kinetic energy of flowing supercurrentson a discretized cubic grid

coupling on bond i

phase of superconducting wavefunction

magnetic vector potential

density of magnetic flux quanta = vortex line densitypiercing plaquette of the cubic grid

uniform magnetic field along z directionmagnetic field is quenched

weakly coupled xy planes

constant couplings between xy planes || magnetic field

random uncorrelated couplings within xy planes disorder strength p

T Temperature

p disorder strengthvortex lattice

liquid

1st order melting

vortex glass

2nd order glass

pc

Equilibrium Behavior

critical pc

at low temperature

p < pc orderedvortex lattice

p > pc disorderedvortex glass

we will be investigating p > pc

Resistively-Shunted-Junction Dynamics••••••••••••••••RInoise••xθiθ +i Itotal

Units

current density:

time:

voltage/length:

temperature:

apply: current density Ix

response:voltage/length Vx

vortex line drift vy

twisted boundary conditions

voltage/length

new variable with pbc

stochastic equations of motion

RSJ details

Previous Simulations

Domínguez, Grønbech-Jensen and Bishop - PRL 78, 2644 (1997)vortex density f = 1/6, 12 ≤ L ≤ 24, Jz = J weak disorder ??moving Bragg glassvortex lines very dense, system sizes small, lines stiff

Chen and Hu - PRL 90, 117005 (2003)

vortex density f = 1/20, L = 40, Jz = J weak disorder p ~ 1/2 pc

moving Bragg glass with 1st order transition to smecticsingle system size, single disorder realization, based on qualitative analysis of S(k)

Nie, Luo, Chen and Hu - Intl. J. Mod. Phys. B 18, 2476 (2004)

vortex density f = 1/20, L = 40, Jz = J strong disorder p ~ 3/2 pc

moving Bragg glass with 1st order transition to smecticsingle system size, single disorder realization, based on qualitative analysis of S(k)

We re-examine the nature of the moving state for strong disorder, p > pc, using finite size analysis and averaging over many disorders

Quantities to Measure

structural

dynamic use measured voltage drops to infer vortex linedisplacements

Parameters

vortex density f = 1/12

Jz = J

p = 0.15 > pc ~ 0.14

L up to 96

ground state p = 0Ix Vx

vortex linemotion vy