Current distribution of collective thermal depinning of Josephson vortices in naturally stacked Josephson junctions

We investigated the thermal-depinning current $\left(I_c\right)$ distribution of Josephson vortices (JVs) in naturally stacked ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ intrinsic Jospehson junctions in tesla-range magnetic fields and at different field tilt angles from the in-plane position. The $I_c$ distribution in the thermal-activation regime contains accurate information on the bias and magnetic-field dependence of the Josephson-vortex pinning potential. In a few-tesla-range magnetic field, JVs in a row in a junction, strongly coupled with each other, are pinned or depinned like a single physical entity at a single pinning center. In the best-aligned in-plane magnetic field, the edge pinning is most relevant and is insensitive to the field strength. In the presence of pancake vortices (PVs) in a slightly tilted field, however, the PV pinning deepens the JV pinning potential linearly with the number of PVs.

Figure 1

(Color online) Zero-field current-voltage $\left(I\text{−}V\right)$ characteristics of the sample stack of ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ intrinsic Josephson junctions. Inset: two-probe measurement configuration with the sample stack sandwiched between two gold electrodes.

Figure 2

(Color online) $I\text{−}V$ characteristics of Josephson-vortex-flow branches in an in-plane magnetic field of $H_{\parallel }=4.5\text{T}$ at $\text{T}=4.6\text{K}$. In the schematics, a row of circles with (without) an arrow represents moving (pinned-down) JVs in a junction. Upper inset: schematic of the sample geometry showing the in-plane field direction. Lower inset: oscillatory vortex-flow magnetoresistance in in-plane fields for a bias current of $1.0\mu \text{A}$ at $T=65\text{K}$. The field periodicity corresponds to adding one Josephson vortex per two natural Josephson junctions.

Figure 3

(Color online) (a) Variation in the microresistor-type pinning potential in Eq. (1) for varying current bias. $\Delta U$ is the pinning potential barrier for a row of Josephson vortices. (b) Depinning current distribution of the second-to-the-rightmost Josephson-vortex-flow branch at different temperatures (upper panel) and the corresponding escaping rate $\Gamma$ (lower panel). Inset: temperature dependence of the standard deviation of the depinning current distribution. Solid lines are best fits to Eqs. (2, 3, 4). (c) $\text{ln}\left(\Gamma \right)$ vs $1/T$ plot for selected bias currents.

Figure 4

(Color online) (a) Magnetic-field dependence of the pinning potential barrier $\Delta U$ at the in-plane position. (b) Magnetic-field tilt-angle dependence of $\Delta U$ at a fixed magnetic field of $H_{\parallel }=6.25\text{T}$. (c) $\Delta U$ vs $1-I/I_c$ in varying fields at the in-plane position. (d) $\Delta U$ vs $1-I/I_c$ in $H_{\parallel }=6.25\text{T}$ for varying field tilt angles. Solid line is a guide to eyes for the slope of 3/2.

Figure 5

(Color online) (a) $I\text{−}V$ characteristics at $H=4.0\text{T}$ and $T=65\text{K}$ for varying magnetic-field tilt angles. The arrow indicates an excess current required to compensate the slowing-down of the Josephson vortex motion by pancake vortices. (b) The excess current normalized by the out-of-plane component of magnetic field $H_{\perp }$ with the best-fit to Eq. (5) (dashed curve). (c) Solid lines (symbols) are tilt-angle dependence of $G_{\text{PV}}\times n_{\text{JV}}^2$ (of the pinning barrier induced by PV in the zero-bias limit) in three different magnetic fields. For clarity, each set of data is shifted vertically by 200 K for $U_0^{\text{PV}}$ (or 453 mS for $G_{\text{PV}}\times n_{\text{JV}}^2$). (d) Relation between enhancement of zero-bias pinning barrier due to PV $U_0^{\text{PV}}\left(\theta \right)$ and $G_{\text{PV}}\times n_{\text{PV}}^2$. The black solid line is a linear fit with the slope of $2.27\left(\pm 0.11\right)\text{K}/\text{mS}$.