View
32
Download
0
Category
Tags:
Preview:
DESCRIPTION
Vortex Line Ordering in the Driven 3-D Vortex Glass. Peter Olsson Umeå University Umeå, Sweden. Ajay Kumar Ghosh Jadavpur University Kolkata, India. Stephen Teitel University of Rochester Rochester, NY USA. Vortex Wroc ł aw 2006. Outline. - PowerPoint PPT Presentation
Citation preview
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
Outline
• The problem: driven vortex lines with random point pins
• The model to simulate: frustrated XY model with RSJ dynamics
• Previous results
• Our resultseffects of thermal vortex rings on large drive meltingimportance of correlations parallel to the applied field
• Conclusions
• Koshelev and Vinokur, PRL 73, 3580 (1994)
motion averages disorder ⇒ shaking temperature ⇒ ordered driven state
• Giamarchi and Le Doussal, PRL 76, 3408 (1996)
transverse periodicity ⇒ elastically coupled channels ⇒ moving Bragg glass
• Balents, Marchetti and Radzihovsky, PRL 78, 751 (1997); PRB 57, 7705 (1998)
longitudinal random force remains ⇒ liquid channels ⇒ moving smectic
• Scheidl and Vinokur, PRE 57, 2574 (1998)• Le Doussal and Giamarchi, PRB 57, 11356 (1998)
We simulate 3D vortex lines at finite T > 0.
uniform drivingforce
Driven vortex lines with random point pinning
For strong pinning, such that thevortex lattice is disordered in equilibrium, how do the vortex linesorder when in a driven steady statemoving at large velocity?
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 driven steady states for 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 glass - algebraic correlations both transverse and parallel to motionvortex 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
at large drives 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
at large drives 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
Parameters
p = 0.15 > pc ~ 0.14
Jz = J
L up to 96
vortex density f = 1/12
ground state p = 0Ix Vx
vortex linemotion vy
Quantities to Measurestructural
dynamic use measured voltage drops to infer vortex linedisplacements
ln S(k, kz=0)
Ix Vx
vortex linemotion vy
Phase Diagram
Previous results of Chen and Hu p ~ 1/2 pc weak disorder
a, b - “moving Bragg glass” algebraic correlations both transverse and parallel to motion
a´, b´ - “moving smectic”
We will more carefully examine the phases on either side of the 1st order transition
Digression: thermally excited vortex rings
melting of ordered state upon increasing current I is due to proliferation of thermally excited vortex rings
I
F(R) ~ RlnR - IR2
ring expands when
R > Rc ~ 1/Ifrom superfluid 4He
rings proliferate
when F(Rc) ~ T ~ 1/I
Tm
+−
Disordered state above 1st order melting Tm
Tm
ln S(k)
vortex linemotion vy
When we increase the system size, the height of the peaksin S(k) along the kx axis do NOT increase only short⇒ranged translational order.
⇒ disordered state is anisotropic liquid and not a smectic
I = 0.48, T = 0.13
Ordered state below 1st order melting Tm
ln S(k)
vortex line motion vy
C(x, y, z=0)
Bragg peak at K10 ⇒ vortex motion is in periodically spaced channels
peak at K11 sharp in ky direction ⇒ vortex lines periodic within each channel
peak at K11 broad in kx direction ⇒ short range correlations between channels
⇒ ordered state is a smectic not a moving Bragg glass
I = 0.48, T = 0.09
Correlations between smectic channels
short ranged translational correlations between smectic channels
Correlations within a smectic channel
C(x, y, z=0)
exp decay to const > 1/4algebraic decay to 1/4
correlations within channel are either long ranged, or decay algebraically with a slow power law ~ 1/5
averaged over 40random realizations
Correlations along the magnetic fieldsnapshot of single channel
z ~ 9
As vortex lines thread the system along z, they wander in the direction of motion y a distance of order the inter-vortex spacing.Vortex lines in a given channel may have a net tilt.
Dynamics
y0(t) y3(t) y6(t) y9(t)
center of mass displacementof vortex lines in each channel
Channels diffuse with respect to one another.
Channels may have slightly different average velocities.
Such effects lead to the short range correlations along x.
36 x 96 x 96
Dynamics and correlations along the field direction z
See group of strongly correlated channels moving together.
Smectic channels that move together are channels in which vortex linesdo not wander much as they travel along the field direction z.
Need lots of line diffusion along z to decouple smectic channels.As Lz increases, all channels decouple.
Only a few decoupled channels are needed to destroy correlations along x.
smaller system: 48 x 48 x48
Behavior elsewhere in ordered driven state
I=0.48, T=0.07, L=6020 random realizations
transverse correlations
Many random realizations have short ranged correlations along x.These are realizations where some channels have strong wandering along z.
Many random realizations have longer correlations along x; x ~ LThese are realizations where all channels have “straight” lines along z.
More ordered state at low T? Or finite size effect?
So far analysis was for I=0.48, T=0.09 just below peak in Tm(I)
Conclusions
For strong disorder p > pc (equilibrium is vortex glass)
• Driven system orders above a lower critical driving force
• Driven system melts above an upper critical force due to thermal vortex rings
• 1st order-like melting of driven smectic to driven anisotropic liquid
• Smectic channels have periodic (algebraic?) ordering in direction parallel to motion, short range order parallel to applied field; channels decouple (shortrange transverse order)
• Importance of vortex line wandering along field direction for decoupling ofsmectic channels
• Moving Bragg glass at lower temperature? or finite size effect?
Recommended