Phase sticking in one-dimensional Josephson junction chains

We studied current-voltage characteristics of long one-dimensional Josephson junction chains with Josephson energy much larger than charging energy, $E_J\gg E_C$. In this regime, typical I-V curves of the samples consist of a supercurrent-like branch at low-bias voltages followed by a voltage-independent chain current branch, $I_{\mathrm{chain}}$ at high bias. Our experiments showed that $I_{\mathrm{chain}}$ is not only voltage-independent but it is also practically temperature-independent up to $T=0.7T_C$. We have successfully model the transport properties in these chains using a capacitively shunted junction model with nonlinear damping.

Figure 1

(a) Optical microscope images of a Josephson junction chain. The chain consists of 2888 SQUIDS with total length $500\mu \mathrm{m}$. Shunt capacitors with the sizes $1000\mu \mathrm{m}\times 800\mu \mathrm{m}$ are placed to the input and output of the chain. (b) Scanning electron microscope (SEM) images of SQUID chains together with termination lead. (c) A group of SQUIDs that consists of two parallel Josephson junctions with the dimensions $300\mathrm{nm}\times 100\mathrm{nm}$.

Figure 2

Schematic diagram of the measurement circuit.

Figure 3

Experimental (a) and simulated (b) dc I-V curves of a long Josephson junction chain with $N=2888$ SQUIDs, $E_{J0}/E_C=36$ at zero magnetic field and $R_Q/R_N\cong 13$. $I_C=634\mathrm{nA}$ is the Ambegaokar-Baratoff critical current for a single junction in this chain,[23] and superconducting energy gap of Al is ${\Delta }_0=200\mu \mathrm{eV}$.

Figure 4

Phase-space diagram of a single junction from the RCSJ model with $Q=5$ and $I=0.5I_C$.

Figure 5

A circuit model of the SQUID chain. Damping is provided by the linear resistors terminating each end of the chain, which model reflection-less transmission lines, and by a nonlinear resistance parallel with each junction. The SQUID junctions are modeled as ordinary Josephson junctions with tunable $E_J$.

Figure 6

(a) $I_{\mathrm{chain}}/I_C$ vs ${\beta }_N=Q^2$ for various samples. Each data point represents the measurement of a different sample at zero magnetic field. The I-V curves in (b) and (c) are of the samples marked with the arrows.

Figure 7

(a) $I_{\mathrm{chain}}$ as a function of ${\beta }_N$. For three different values of ${\beta }_N$, we plot the dc I-V curves (a1,b1,c1) and grey-scale plots of the phase slips (a2,b2,c2) across the Josephson junction chains as a function of bias voltage. The grey-scale bar gives the number of phase slips in the fixed simulation time.

Figure 8

(a) I-V curves of a sample ($N=2888$, ${\beta }_N\approx 1$, $E_{J0}/E_C\approx 88$, and $E_{J0}/k_B\approx 90$ K) at zero magnetic field with various temperatures. (b) Simulated I-V curves with the same sample parameters.

Figure 9

(a) High-voltage characteristics of the sample shown in Fig. 3. (b) Differential conductance $dI/dV$, (c) simulated dc I-V curve, and (d) the simulated $dI/dV$ of the same sample. The arrows shows the direction of the sweep.

Figure 10

Simulated dc I-V curve (a) and distribution of phase slips (b) and (c) for the sample shown in Figs. 3 and 9.