Driven flux-line lattices in the presence of weak random columnar disorder: Finite-temperature behavior and dynamical melting of moving Bose glass

We use three-dimensional numerical simulations to explore the phase diagram of driven flux-line lattices in the presence of weak random columnar disorder at finite temperature and high driving force. We show that the moving Bose glass phase exists in a large range of temperature up to its melting into a moving vortex liquid. It is also remarkably stable upon increasing velocity. The dynamical transition to the correlated moving glass expected at a critical velocity is not found at any velocity accessible to our simulations. Furthermore, we show the existence of an effective static tin roof pinning potential in the direction transverse to motion, which originates from both the transverse periodicity of the moving lattice and the localization effect due to the correlated disorder. Using a simple model of a single elastic line in such a periodic potential, we obtain a good description of the transverse field penetration at surfaces as a function of thickness in the moving Bose glass phase.

Figure 1

(Color online) (a) Average vortex line inclination versus field inclination at $T={10}^{-4}$ for $v={10}^{-2}$, $N_v=30$, and several thicknesses (circles) compared with disorder free linear response (squares). Inset: average shape of a line at low inclination for $N_z=149$ and $T={10}^{-10}$ (thick brown line) and sinh fit (thin dashed blue line). (b) Slope $d\left(\text{tan}{\theta }_B\right)/d\left(\text{tan}{\theta }_H\right)$ at low angle versus $N_z$ for $T={10}^{-10}$ (red circles) and $T={10}^{-4}$ (green triangles). The solid blue line is the $\text{tanh}\left(\frac{L}{2z_0}\right)/L$ fit; the dashed green line is the $N_z^{-1}$ dependence at large $N_z$.

Figure 2

(Color online) $C_V=\frac{⟨E_t^2⟩-{⟨E_t⟩}^2}{k_B{T}^2}$ with $k_B=1$ for $N_z=49$ (blue squares) and slope of the transverse induction response $d\left(\text{tan}{\theta }_B\right)/d\left(\text{tan}{\theta }_H\right)$ at low angle versus temperature for $N_z=19,29,49$ (red circles) compared with the pinning free case (green triangles), both for $N_V=30$ and $v={10}^{-2}$.

Figure 3

(Color online) (a) $C_V$ (blue squares), height of the correlation function first-neighbor peaks (red circles), and background level (green triangles) versus temperature for $N_V=120$, $N_z=19$, and $v={10}^{-2}$. (b) Amplitude of the in-plane correlation function along the $x$ axis just below ($T=2.1\times {10}^{-4}$: red line) and above ($T=2.2\times {10}^{-4}$: dashed blue line) the transition.

Figure 4

(Color online) (a) $B_2\left(z_{ij}\right)=⟨{\left(y_i-y_j\right)}^2⟩$ ($z_{ij}$ is expressed in units of layer spacing $s$) for $T$ from ${10}^{-4}$ to ${10}^{-3}$, $N_V=30$, $N_z=149$, and $v={10}^{-2}$. Inset: $B_2\left(z_{ij}\right)$ versus $T$ for $z_{ij}=10\text{s}$ (green circles) and $z_{ij}=100\text{s}$ (red squares). (b) From top to bottom: total energy, amplitude of the correlation function at the first-neighbor peaks, and $B_2\left(L/2\right)$ versus time close to melting for $N_V=120$, $N_z=29$, and $v={10}^{-2}$.