Numerical Simulation Evidence of Dynamical Transverse Meissner Effect and Moving Bose Glass Phase

We present 3D numerical simulation results of moving vortex lattices in the presence of 1D correlated disorder at zero temperature. Our results with field tilting confirm the theoretical predictions of a moving Bose glass phase, characterized by transverse pinning and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. Beyond a critical transverse field, vortex lines exhibit along all their length a “kink” structure resulting from an effective static “tin roof” pinning potential in the transverse direction.

Figure 1

Average vortex line inclination $\tan {\theta }_B=B_y/B_z$ versus the field inclination $\tan {\theta }_H=H_y/H_z$ for several system sizes $N_z=19,29,39,49,149$ (filled circles). The linear response of the pinning free vortex system is shown with open circles. Size effects show the existence of a critical transverse field $H_y^c/H_z\sim 0.50$ below which the DTME is observed. Inset: projection in the $(y,z)$ plane of the 30 vortex lines composed of $N_z=149$ layers for $H_y/H_z\sim 0.47$ illustrating the MBoG phase (thick lines) and DTME, compared to the vortex lines of the nondisordered system (thin oblique lines).

Figure 2

Plateaus and hysteresis observed above the transition for $N_z=49$. The origin of each plateau is connected to a given number of pinned regions passed through by each vortex line. For details about the plateau labels and the pinned regions defining the effective static pinning landscape, see Fig. 3 and the text . The plateaus and hysteresis disappear in the infinite thickness limit $N_z\to \infty$.

Figure 3

(a) Projection in the $(y,z)$ plane of the 30 moving vortex lines composed of $N_z=149$ layers and obtained for $H_y/H_z\sim 0.53$ while increasing the transverse field. In grey are materialized the pinned regions which define an effective pinning landscape which is static and almost periodic. (b) Derivative $dz/dy$ for all the 30 vortex lines shown in (a).

Figure 4

Plateaus and hysteresis observed within the simple model [Eq. (1)] for a finite length $L=0.4a_0$ and $g/c=18.75$. The solid circles represent the metastable states followed by the elastic line when the surface force $f$ is slowly increased then decreased. The open circles represent the true equilibrium states. The straight line displays the pure elastic response $g=0$. Inset: Eq. (1) results in the infinite size limit $L\to \infty$ showing the disappearance of the plateaus and hysteresis even though the kink structure still exists.