Metastable behavior of vortex matter in the electronic transport processes of homogenous superconductors

We study numerically the effect of vortex pinning on the hysteresis voltage-temperature $\left(V\text{−}T\right)$ loop of vortex matter. It is found that different types of the $V\text{−}T$ loops result from different densities of vortex pinning center. An anticlockwise $V\text{−}T$ loop is observed for the vortex system with dense pinning centers, whereas a clockwise $V\text{−}T$ loop is brought about for vortices with dilute pinning centers. It is shown that the size of the $V\text{−}T$ loop becomes smaller for lower experimental speed, higher magnetic field, or weak pinning strength. Our numerical observation is in good agreement with experiments.

Figure 1

(a) Typical anticlockwise $V\text{−}T$ loop (solid triangles) and the corresponding $N_{\mathrm{v}}^{\mathrm{p}}∕N_{\mathrm{v}}\text{−}T$ loop (open triangles). $N_{\mathrm{v}}^{\mathrm{p}}$ is the number of pinned vortices. The temperature is varied in the direction indicated by the arrows. Solid lines are guide for eyes. (b) The vortices (open circles) and pinning centers (crosses) at position $B$ in (a). (c) The vortices (open circles) and pinning centers (crosses) at position $C$ in (a).

Figure 2

Effect of the TSS on the $V\text{−}T$ loop. $B=0.007B_{\mathrm{c}20}$, $N_p=N_v$, $f_{pv0}=9f_0$. TSS affects only the size of the $V\text{−}T$ loops but not their direction.

Figure 3

Effect of the field on the $V\text{−}T$ loop. $dT∕dt=0.04T_c∕t_0$, $f_{pv0}=9f_0$, $B=0.007B_{\mathrm{c}20}$ (dashed lines), $0.028B_{\mathrm{c}20}$ (dotted lines), and $0.056B_{\mathrm{c}20}$ (solid lines) corresponding to $N_p=N_v$, $0.25N_v$, and $0.125N_v$. Inset: The $V\text{−}T$ loops for different initial vortex states. $dT∕dt=0.04T_c∕t_0$, $f_{pv0}=9f_0$, $N_p=N_v$, and $B=0.007B_{\mathrm{c}20}$. The field affects only the size of the $V\text{−}T$ loops but not their direction.

Figure 4

Typical clockwise $V\text{−}T$ loop (solid triangles) and the corresponding $N_{\mathrm{v}}^{\mathrm{p}}∕N_{\mathrm{v}}\text{−}T$ curve (open triangles) for a systems with dilute pinning centers. $B=0.007B_{\mathrm{c}20}$, $N_p=0.1N_v$, $dT∕dt=0.001T_c∕t_0$, and $f_{pv0}=90f_0$. Inset: Steady channel flow forms in the warming branch from $0.5T_c$ to $0.91T_c$. The circles and lines represent the random pinning centers and vortex trajectories, respectively.

Figure 5

Effect of pinning force strength $f_{pv0}$ on the $V\text{−}T$ loops. $B=0.007B_{\mathrm{c}20}$, $N_p=0.1N_v$, $dT∕dt=0.001T_c∕t_0$, $f_{pv0}=\left(\text{right}\right)$ $60f_0$, $45f_0$, $30f_0$ (left). The size of the $V\text{−}T$ loop becomes smaller with the decrement of $f_{pv0}$, but its direction does not change.

Figure 6

Effects of the vortex pinning density on the $V\text{−}T$ loops. $B=0.007B_{\mathrm{c}20}$, $dT∕dt=0.001T_c∕t_0$, $N_p{f}_{pv0}∕N_{\mathrm{v}}\equiv 9f_0$. The direction of the $V\text{−}T$ loops depends on the vortex pinning density.