Scaling behavior of the crossover to short-stack regimes of Josephson vortex lattices in ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ stacks

We report the systematic investigations of the oscillation of the Josephson vortex (JV) flow resistance in ${\text{Bi}}_2{\text{Sr}}_2{\text{CaCu}}_2{\text{O}}_{8+\delta }$ microfabricated junctions with various geometries and superconducting anisotropy parameters. As the applied magnetic field parallel to the $ab$ plane is increased, oscillation with a period corresponding to a half flux quantum par atomic Josephson junction changes to oscillation with a doubled period. This crossover is scaled by both the junction length and the anisotropy parameter indicating that the bulk inductive coupling that favors the triangular JV lattice is replaced with the surface deformation energy as the dominant interaction for a JV lattice. These results suggest that the in-phase square JV lattice is pronounced at a higher magnetic field in a smaller and more anisotropic sample.

Figure 1

(Color online) Field dependence of differential $c$-axis resistivity in B19 (a) and P52 (b) at 60 K. Solid symbols represent differential resistance $dV/dI$ obtained from $IV$ characteristics. Broken curves connect maxima and minima points in $\rho \left(H\right)$. In the inset of (b), solid curve indicates Ohmic resistances $V/I$ obtained by sweeping magnetic field at $I=1.2\mu \text{A}$. Blue vertical grids in (a) and inset of (b) indicate that the fields of $H/H_0$ are integers.

Figure 2

(Color online) (a) $IV$ characteristics at 60 K in V31 $\left(T_c=84\text{K}\right)$ at various magnetic fields from 0 (top) to 60 kOe (bottom). (b) Field dependence of $I_1$, current at $V=2\text{mV}$ [the arrow in (a)], at 60, 75, 80, and 82 K from top to bottom. Inset shows temperature dependence of anisotropy parameter $\gamma$ obtained by Eq. (1).

Figure 3

(Color online) $L$ dependence of crossover field $H_{1/2}$ in which $\gamma$ is renormalized. Inset: method to extract $H_s$ and $H_{1/2}$. Solid and broken curves are those in Fig. 1b normalized by $R_{\text{max}}$ [red (dark gray) broken curve].