Reentrant dynamics of driven pancake vortices in layered superconductors

The dynamics of driven pancake vortices in layered superconductors is studied using molecular-dynamics simulations. We found that, with increasing driving force, for strong interlayer coupling, the preexisted vortex lines either directly depin or first transform to two-dimensional (2D) pinned states before they are depinned, depending on the pinning strength. In a narrow region of pinning strengths, we found an interesting repinning process, which results in a negative differential resistance. For weak interlayer coupling, individually pinned pancake vortices first form disordered 2D flow and then transform to ordered three-dimensional (3D) flow with increasing driving force. However, for extremely strong pinning, the random pinning-induced thermal-like Langevin forces melt 3D vortex lines, which results in a persistent 2D flow in the fast-sliding regime. In the intermediate regime, the peak effect is found: With increasing driving force, the moving pancake vortices first crystallize to moving 3D vortex lines, and then these 3D vortex lines are melted, leading to the appearance of a reentrant 2D flow state. Our results are summarized in a dynamical phase diagram.

Figure 1

The average velocity $\langle v\rangle$ (upper panels) and correlation function $c_z$ (lower panels) versus driving force $f_d$ for coupling strength $s_m=32$, and pinning strength (a) $f_p=0.2$ and (b) $f_p=0.8$. Black (red) lines correspond to increasing (decreasing) $f_d$.

Figure 2

The average velocity (a) $\langle v\rangle$, the fraction of depinned vortices, (b) $\gamma$, and the correlation function (c) $c_z$ versus driving force $f_d$ for $f_p=0.38$ and $s_m=18$. Black (red) lines correspond to increasing (decreasing) $f_d$.

Figure 3

The average velocity $\langle v\rangle$ (upper panels) and correlation function $c_z$ (lower panels) versus driving force $f_d$ for coupling strength $s_m=2$ and pinning strength (a) $f_p=0.2$ and (b) $f_p=0.8$. Black (red) lines corresponding to increasing (decreasing) $f_d$.

Figure 4

The average velocity $\langle v\rangle$ (black line) and correlation function $c_z$ (blue/gray line) versus driving force $f_d$ for coupling strength $s_m=4$ and pinning strength (a) $f_p=2.7$, (f) $f_p=3.0$, and (g) $f_p=3.5$. Projections of the positions of pancake vortices for (b) $f_d=1.84$, (c) $f_d=5.84$, (d) $f_d=9.02$, and (e) $f_d=21.3$.

Figure 5

The RDF for (a) $f_d=1.84$, (b) $f_d=5.84$, (c) $f_d=9.02$, and (d) $f_d=21.3$, corresponding to projections shown in Figs. 4–4, respectively. (e) The correlation functions $c_{xy}$ (red/gray line) and $c_z$ (black line) versus driving force $f_d$ for coupling strength $s_m=4$ and pinning strength $f_p=2.7$.

Figure 6

(a) The correlation function $\langle c_z\rangle$ (black line) and $c_{xy}$ (red/gray line) versus driving force $f_d$ for coupling strength $s_m=4$ and pinning strength $f_p=2.7$. (b) Projections of pancake vortices' positions for $f_d=5.84$.

Figure 7

The dynamical phase diagram in the plan of interlayer coupling strength $s_m$ versus pinning strength $f_p$ for increasing driving force $f_d$. 3DP, 2DP, 3DF, and 2DF are abbreviations for 3D pinned, 2D pinned, 3D flow, and 2D flow, respectively. The blue area marked by NDR is where we found NDR in which dynamical regimes are including 3D pinned, 3D flow, 2D pinned, and reentrant 3D flow.