Investigation of the breakpoint region in stacks with a finite number of intrinsic Josephson junctions

We study the breakpoint region on the outermost branch of the current-voltage characteristics of stacks with different numbers of intrinsic Josephson junctions. We show that at periodic boundary conditions the breakpoint region is absent for stacks with an even number of junctions. For stacks with an odd number of junctions and for stacks with nonperiodic boundary conditions the breakpoint current increases with the number of junctions and saturates at a value corresponding to the periodic boundary conditions. The region of saturation and the saturated value depend on the coupling between the junctions. We explain the results by the parametric resonance at the breakpoint and excitation of a longitudinal plasma wave by Josephson oscillations. A method for diagnostics of the junctions in the stack is proposed.

Figure 1

(Color online) IVC of the outermost branch for stacks with different numbers $N$ of IJJs at $\gamma =$ (a) 0 and (b)1.

Figure 2

(Color online) IVC of the outermost branch for stacks with different numbers of junctions at periodic BCs.

Figure 3

(Color online) (a) $N$ dependence of $I_{bp}$ for $\gamma =0$ (curve 1) and periodic (curve 2) boundary conditions at different $\alpha$; (b) $N$ dependence of the BPR width $w_{bp}$ for stacks with even and odd numbers of junctions at $\gamma =0$ (1) and periodic (2) boundary conditions.

Figure 4

(Color online) (a) Parametric resonance region in $\Omega \left(k\right)-\beta \left(k\right)$ diagram. Black dots (stripe) correspond to the breakpoint current $I_{bp}$ in the IVC for $k=\pi$ at different values of parameters $\alpha$ and $\beta$. (b) Charge on the S layers in the stacks with 10 (b1) and 11 (b2) IJJs at periodic BCs and with 10 IJJs at $\gamma =1$ (b3).

Figure 5

(Color online) BPR on the branches of the IVC of stacks with one oscillating junction in the case of ten IJJs at $\alpha =1$, $\beta =0.2$, and $\gamma =0$. The top curve corresponds to the real scale of voltage, but the others are shifted down for clarity by two units.