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Applied Physics Letters

Sensitivity of a DC SQUID with a non-sinusoidal current-phase relation in its junctions

Jonathan R. Prance, Michael D. Thompson

Published May 29, 2023• 1 citation
Publisher

Abstract

In ballistic superconductor–normal metal–superconductor Josephson junctions, such as those made from graphene or high mobility semiconductors, the current-phase relation may not have the common, sinusoidal form but can be skewed to have a peak supercurrent at a phase difference greater than π/2. Here, we use a numerical simulation that includes thermal noise to investigate the sensitivity of a DC superconducting quantum interference device (SQUID) with such junctions. The simulation uses a resistively and capacitively shunted junction model where the current-phase relation of each junction can be defined as an arbitrary function. The modulation, transfer function, noise, and sensitivity of a SQUID are calculated for different types of current-phase relation. For the examples considered here, we find that the flux sensitivity of the SQUID is always degraded by forward skewing of the current-phase relation, even in cases where the transfer function of the SQUID has been improved.

DOI
10.1063/5.0151607

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In ballistic superconductor–normal metal–superconductor Josephson junctions, such as those made from graphene or high mobility semiconductors, the current-phase relation may not have the common, sinusoidal form but can be skewed to have a peak supercurrent at a phase difference greater than π/2. Here, we use a numerical simulation that includes thermal noise to investigate the sensitivity of a DC superconducting quantum interference device (SQUID) with such junctions. The simulation uses a resistively and capacitively shunted junction model where the current-phase relation of each junction can be defined as an arbitrary function. The modulation, transfer function, noise, and sensitivity of a SQUID are calculated for different types of current-phase relation. For the examples considered here, we find that the flux sensitivity of the SQUID is always degraded by forward skewing of the current-phase relation, even in cases where the transfer function of the SQUID has been improved.
We present measurements of DC superconducting quantum interference devices based on Nb/graphene/Nb Josephson junctions. The superconducting proximity effect in graphene can be used to build Josephson junctions whose critical current can be controlled by field-effect gates. These junctions combine the tunability of semiconductor Josephson junctions with the high critical currents and low contact resistances of metal SNS junctions. By using local gates, the SQUID junction critical currents can be modified individually and this allows the sensitivity and symmetry of the SQUID to be controlled in-situ. We compare the critical current of the SQUID with simulations that include a non-sinusoidal current phase relation in the junctions, as expected for ballistic graphene junctions. We also investigate the transfer function of the device in both symmetric and asymmetric configurations and find a highest transfer function of 300 μV/Φ0. Graphene Josephson junctions have the potential to add functionality to existing technologies; for example, to make SQUID magnetometers with tunable sensitivity or superconducting qubits with fast electrical control.
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
Properties of white noise of a high-Tc dc superconducting quantum interference device (SQUID) have been studied using numerical simulation. It is shown that thermal noise at T=77 K significantly affects the noise properties of the SQUID. As a result, dependencies of noise properties on inductance become quite different from conventional results at T=4.2 K. In contrast to the case T=4.2 K, the voltage noise of the SQUID at T=77 K depends very weakly on the inductance, while the transfer function degrades rapidly with inductance. Consequently, rapid degradation of flux noise with inductance, as compared with the case T=4.2 K, is caused mainly by that of the transfer function. These simulation results explain reasonably experimental results reported recently. Therefore, it is necessary to improve the transfer function for the improvement of noise properties in the case of large inductances. Numerical simulation shows that a method for improving the transfer function using resistively shunted inductance or three Josephson junctions, which was proposed by the authors, is also useful for improving noise properties in the case of large inductances.
Superconducting quantum interference devices (SQUIDs) based on nanobridge junctions (NBJs) are promising platforms for highly sensitive magnetic detection. The SQUID performance is influenced by the non-sinusoidal current-phase relation (CPR) of NBJs. In this work, we measured the flux modulation of 10 asymmetric Nb SQUIDs based on three-dimensional NBJs, along with the CPR response in each device, which is mainly determined by the junction with the smaller critical current. By studying the CPR parameters (skewness Δ θ , critical current I c1 , and effective junction inductance L j ), together with the SQUID modulation characteristics (voltage modulation amplitude Δ I c R n and current modulation ratio Δ I c /2 I c1 ), we found that as I c1 increases from 0.6 μA to 6.6 μA and L j correspondingly decreases from 106 pH to 70 pH, the CPR skewness Δ θ increases from 0.2 rad to 1.5 rad. Over this range, Δ I c /2 I c1 decreases from 1.2 to 0.5, while Δ I c R n increases from about 0.06 mV to 0.22 mV. More specifically, Δ I c R n increases while Δ I c /2 I c1 decreases with increasing I c1 , whereas both quantities decrease with increasing L j . These results reveal a trade-off between intrinsic SQUID response and tolerance to readout noise, suggesting that improved performance can be achieved by engineering NBJs with increased I c1 and smaller L j .
Superconducting quantum interference devices (SQUIDs) are promising for detection of extremely weak power regimes for the Internet of Things and long-distance satellite networks. In low-frequency magnetic signal measurements, it has demonstrated superior performance over the traditional systems. We review the resistively and capacitively shunted junction model of dc SQUIDs and investigate its transfer function to magnetic flux signals while taking thermal fluctuation into account. We numerically evaluate the influence of bias current and bias flux signal to determine the operating parameters of the device. The performances related to SQUID ring inductance operating at 4.2 K and 77 K are demonstrated. Combined with common radio frequency front-end modules, including low-noise amplifier and low-pass filter, we evaluate the bit-error-rate performance of the system under different inductance values and inferred that the sensitivity of the system can reach −99 dBm at 100 MHz bandwidth.