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Vortex Line Ordering in the Driven 3-D Vortex Glass

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. MesoSuperMag 2006. Driven vortex lines with random point pinning.

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Vortex Line Ordering in the Driven 3-D Vortex Glass

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  1. 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 MesoSuperMag 2006

  2. Driven vortex lines with random point pinning For strong pinning, such that the vortex lattice is disorderedin equilibrium, how do the vortex lines order when in a driven steady state moving at large velocity? • • 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.

  3. 3D Frustrated XY Model kinetic energy of flowing supercurrents on a discretized cubic grid uniform magnetic field along z direction; magnetic field is quenched: vortex line density uniform couplings between xy planes || magnetic field random uncorrelated couplings within xy planes disorder strength isp weakly coupled xy planes f = 1/12

  4. Equilibrium Phase Diagram (from Monte Carlo simulations) criticalpc at low temperature p < pc ordered vortex lattice p > pc disordered vortex glass we will be investigating driven steady states forp > pc

  5. Driven Steady State Phase Diagram (from Resistively-Shunted-Junction Dynamics) apply: current density Ix response: voltage/length Vx vortex line drift vy Units current density: time: voltage/length: temperature:

  6. Previous Simulations Domínguez, Grønbech-Jensen and Bishop - PRL 78, 2644 (1997) f = 1/6, 12 ≤ L ≤ 24, Jz = J weak disorder ?? claim moving Bragg glass - algebraic correlations vortex lines very dense, system sizes small, lines stiff Chen and Hu - PRL 90, 117005 (2003) f = 1/20, L = 40, Jz = Jweak disorder p ~ 1/2 pc claim moving Bragg glass at large drives with 1st order transition to smectic single system size, single disorder realization Nie, Luo, Chen and Hu - Intl. J. Mod. Phys. B 18, 2476 (2004) f = 1/20, L = 40, Jz = Jstrong disorder p ~ 3/2 pc claim moving Bragg glass at large drives with 1st order transition to smectic single system size, single disorder realization We re-examine the nature of the moving state for strong disorder, p > pc, using finite size analysis and averaging over many disorders

  7. Quantities to Measure structural dynamicuse measured voltage drops to infer vortex line displacements

  8. Driven Steady State Phase Diagram p = 0.15 > pc ~ 0.14 a b Ix Vx vortex line motion vy ln S(k, kz=0)

  9. Disordered state above 1st order melting Tm I = 0.48, T = 0.13 ln S(k) b vortex line motion vy When we increase the system size, the height of the peaks in S(k) along the kx axis do NOT increase ⇒ only short ranged translational order. ⇒ disordered state is anisotropic liquid

  10. vortex line motion vy C(x, y, z=0) Ordered state below 1st order melting Tm I = 0.48, T = 0.09 a ln S(k) 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

  11. short ranged translational correlations between smectic channels Correlations between smectic channels

  12. C(x, y, z=0) averaged over 40 random realizations exp decay to const > 1/4 algebraic decay to 1/4 correlations within channel are either long ranged, or decay algebraically with a slow power law ~ 1/5 Correlations within a smectic channel

  13. Correlations along the magnetic field As vortex lines thread the system along z, they wander in the direction of motion y a distance of order the inter-vortex spacing. Such wanderings important for decoupling of smectic planes. snapshot of single channel z ~ 9

  14. 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 (short range transverse order) • Importance of vortex line wandering along field direction for decoupling of smectic channels • Moving Bragg glass at lower temperature? or finite size effect?

  15. 36 x 96 x 96 y0(t) y3(t) y6(t) y9(t) center of mass displacement of 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. Dynamics

  16. Dynamics and correlations along the field direction z smaller system:48 x 48 x48 See group of strongly correlated channels moving together. Smectic channels that move together are channels in which vortex lines do not wander much as they travel along the field directionz. 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 alongx.

  17. Behavior elsewhere in ordered driven state transverse correlations I=0.48, T=0.07, L=60 20 random realizations Tm So far analysis was forI=0.48,T=0.09 just below peak inTm(I) c c 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 ~ L These are realizations where all channels have “straight” lines along z. More ordered state at low T? Or finite size effect?

  18. Digression: thermally excited vortex rings Tm melting of ordered state upon increasing current I is due to proliferation of thermally excited vortex rings ring expands when R > Rc ~ 1/I I from superfluid 4He rings proliferate whenF(Rc) ~ T ~ 1/I F(R) ~ RlnR- IR2

  19. RSJ details twisted boundary conditions voltage/length new variable with pbc stochastic equations of motion

  20. Previous results of Chen and Hup ~ 1/2pc 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

  21. Outline • The problem: driven vortex lines with random point pins • The model to simulate: frustrated XY model with RSJ dynamics • Previous results • Our results importance of correlations parallel to the applied field • Conclusions

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