Bridging the Gap Between Nanowires and Josephson Junctions: A Superconducting Device Based on Controlled Fluxon Transfer

The basis for superconducting electronics can broadly be divided between two technologies: the Josephson junction and the superconducting nanowire. While the Josephson junction (JJ) remains the dominant technology due to its high speed and low power dissipation, recently proposed nanowire devices offer improvements such as gain, high fanout, and compatibility with CMOS circuits. Despite these benefits, nanowire-based electronics have largely been limited to binary operations, with devices switching between the superconducting state and a high-impedance resistive state dominated by uncontrolled hotspot dynamics. Unlike the JJ, they cannot increment an output through successive switching and their operation speeds are limited by their slow thermal-reset times. Thus, there is a need for an intermediate device with the interfacing capabilities of a nanowire but a faster, moderated response allowing for modulation of the output. We present a nanowire device based on controlled fluxon transport. We show that the device is capable of responding proportionally to the strength of its input, unlike other nanowire technologies. The device can be operated to produce a multilevel output with distinguishable states, the number of which can be tuned by circuit parameters. Agreement between experimental results and electrothermal circuit simulations demonstrates that the device is classical and may be readily engineered for applications including use as a multilevel memory.

Figure 1

Device design and characterization. (a) Scanning electron micrograph of the device. The dark area is the $\mathrm{Nb}\mathrm{N}$ film, while the light outlines are the underlying substrate. The inset shows an enlarged view of the 60-nm-wide constriction in parallel with the resistive shunt. The shunt dimensions are 1 × 3 µm². The righthand side of the loop is connected to a yTron with arm widths equal to 300 nm. (b) Circuit representation of the device. In this particular design, R_s = 5 Ω, L_shunt = 50 pH, L_constriction = 284 pH, and L_loop = 1.87 nH. I_write is the bias current that switches the nanowire constriction (NW) and changes the state of the loop. I_read is the bias current applied to the right arm of the yTron in order to sense the amount of circulating current in the loop. (c) Current-voltage characteristics of an isolated shunted nanowire of width = 60 nm, R_s = 5 Ω. The absence of hysteresis implies that Joule heating through the nanowire has been significantly reduced by the presence of a shunt resistor. Comparison to the characteristics of an unshunted nanowire may be found in the Supplemental Material [20].

Figure 2

Response to the voltage and pulse width of the write input. (a) Switching current of the right yTron arm as a function of the input write voltage for a superconducting loop with an unshunted constriction. The input pulse widths range from 5 ns to 100 µs. The switching currents are plotted in terms of $\mathrm{\Delta }{I}_{\mathrm{sw}}=I_{\mathrm{sw}}-I_{\mathrm{sw}}(v=0)$, where v is the voltage height of the input pulse. The decrease in $\mathrm{\Delta }{I}_{\mathrm{sw}}$ suggests that some flux has been lost in the loop at high input voltages, potentially due to overheating of the constriction. Each point represents the mean of 10 sequential measurements of the yTron switching current. (b) Results from the same measurement repeated on a superconducting loop with a shunted constriction, R_s = 5 Ω. The proportional increase in switching current with increasing input voltage implies that the dynamics of the constriction are controlled by the presence of the shunt resistor. Logarithmic colormaps showing the complete range of input pulse widths and voltages for both devices may be found in the Supplemental Material (see Fig. S7) [20].

Figure 3

Demonstration of controlled flux shuttling. (a) Switching current of the right arm of the yTron on the shunted device in response to a dc bias ramp of $\pm 40\mu \mathrm{A}$ applied to I_write of the constriction. Each point is the mean of 10 measurements of the yTron switching current. Each bias current step in I_write is applied to the constriction for 100 ms before being turned off during the reading operation. (b) Repetition of the same measurement on a device with an unshunted constriction. In comparison to the shunted device, no repeatable intermediate states are observed, and nearly the maximum amount of current is trapped every time the constriction switches. (c) Blue squares represent I_write at the initial point of each of the first 14 steps of the yTron switching current in (a). The approximate circulating loop current I_loop (red squares) is also calculated using I_c = 21 µA. The data shows that the amount of circulating loop current can be incremented in nearly even steps of approximately 5 µA.

Figure 4

Time domain simulations of the circuit highlighting the three branches through which the bias writing current is diverted. (a) Bias current ramp delivered to the device. (b) Current through the shunt resistor. (i) Simulation over a long-time domain. (ii) Simulation over a single switching event. Time on the x axis has been shifted to start from t = 0. In the 1-MΩ case, essentially no current is diverted to the resistor, and the maximum amount of current is stored in the loop. When R_s = 5 Ω, nearly all of the current is diverted to the resistor, reducing the amount of trapped flux. Inset shows that the low shunt resistor also reduces the hotspot resistance and allows it to collapse more quickly. (c) Current through the constriction. (i) Simulation over a long-time domain. (ii) Simulation over a single switching event. (d) Current through the inductor, represented in terms of trapped fluxoids. (i) Simulation over a long-time domain. The amount of flux trapped in the loop increases by 5 ${\mathrm{\Phi }}_0$ every time the constriction switches. (ii) Simulation over a single switching event, showing that the maximum amount of flux is trapped for the device shunted with 1 MΩ. For all of these simulations, L_shunt = 50 pH and L_loop = 1.87 nH.

Figure 5

Simulated effect of circuit parameters on amount of trapped flux. (a) Number of fluxons per switching event as a function of varying R_s and L_shunt. R_s is swept in increments of 1 Ω and L_shunt is swept in increments of 50 pH. L_loop is held constant at 1.87 nH. (b) Number of fluxons per switching event as a function of varying R_s and L_loop. R_s is swept in increments of 1 Ω, and L_loop is swept in increments of 50 pH. L_shunt is held constant at 50 pH. (c) Comparison of the simulated number of fluxons per switching event with the three experimentally measured devices. The orange curve represents the trend for L_loop = 0.65 nH, and the red curve represents the trend for L_loop = 1.85 nH. Experimental mean values are represented as black squares. The error bars are $\pm 0.5\sigma$.