Dynamical Matching of Josephson Vortex Lattice with Sample Edge in Layered High-$T_c$ Superconductors: Origin of the Periodic Oscillation of Flux Flow Resistance

We numerically investigate Josephson vortex flow states in layered high-$T_c$ superconductors motivated by a recent experimental observation for accurate periodic magnetic field dependences of the Josephson vortex flow resistance over a wide range of magnetic field ($0.5–4.0\mathrm{T}$). We confirm in our mesoscale simulations that dynamical matching of Josephson vortex lattice with sample edge is responsible for the periodic dependence. The present simulations reveal that the Josephson vortex lattice flow speed is particularly suppressed when the moment of vortex entry matches that of vortex escape. Thus, the possible matching situations are taken into account and the observed periodicity is successfully explained.

Figure 1

(a) The schematic figure for the simulated region. The periodic boundary condition along the $c$- axis is imposed. The arrows and the dashed lines schematically depict the image of the periodic boundary condition. (b) The simulation results of the magnetic field dependences of dc voltage measured in two stacked junctions $V_{1+2}$ for three different $c$-axis currents. The sample dimension $L$ is $7.5\mu \mathrm{m}$. $L_N$ means the mesh number along the $ab$ plane in the simulation ($L_N=200$).

Figure 2

The sample size effect on the magnetic field dependence of the flux flow voltage for a current $j/j_c=0.038$. (I) The magnetic field dependences of the flux flow voltage measured in two stacked junctions for three size $L=7.5$, 15.0, and $22.5\mu \mathrm{m}$. (II) The comparison of the periodicity $H_p$ between the experiment [8] and the simulation in different sample sizes. The straight line indicates the relation $H_p=\frac{{\varphi }_0}{2LD}$

Figure 3

(I) The schematic view for the local voltage measurements performed in the simulation. (II) The time evolutions of the local voltages, (a) $V_{2L}(t)$, (b) $V_{2C}(t)$, and (c) $V_{2R}(t)$ whose measuring positions are indicated in (I). (III) The schematic figure for the free energy potential in the Josephson vortex flow state under the presence of the edge barrier potential.

Figure 4

The comparisons among the time developments of the local voltages at the three edges (see the upper right panel) for the two minimum points (a),(c) and the one maximum point (b) in (I) the magnetic field dependence of the flux flow voltage. In (a)–(c), the left panel gives a comparison between $V_{2L}(t)$ and $V_{2R}(t)$, the center panel contrasts $V_{2L}(t)$ with $V_{1R}(t)$, and the right panel schematically depicts the corresponding matching moment.