Dynamics of First and Second Switches in Bi$_{2}$ Sr$_{2}$CaCu $_{2}$O$_{8+\delta }$ Intrinsic Josephson Junction Stacks Measured by Specifically Designed Electronics

Abstract

We measure switching probability distributions for the first and the second switches of stacks of Bi 2 Sr 2 CaCu 2 O 8+δ intrinsic Josephson junctions. To measure switching probability distributions, we design a current source and introduced a microcontroller. The resolution and accuracy are sufficient for measuring switching probability distributions of intrinsic Josephson junctions. For the first switch, crossover temperatures between thermally activated escape and macroscopic quantum tunneling are in the range between 0.8 and 2.2 K. The crossover temperatures of the second switch are approximately 8.0 and 6.8 K for the samples with critical densities of 1.0 and 2.0 kA/cm 2 , respectively. We analyze critical current density dependence of the crossover temperature of the second switch. The crossover temperature decreases with increasing critical current density. This anticorrelation can be explained neither by the single-junction model nor by the heating effect. The anticorrelation is a peculiar phenomenon observed in the second switch. We consider that the anticorrelation is attributed to the capacitive coupling. The strength of the capacitive coupling is weaker in IJJs with higher critical current density because the charge screening length is shorter due to increase of carrier density.