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Physica C Superconductivity

Influence of the current-phase relation of nanobridge junction on the SQUID performance

Xinxin Fan, Yue Wang, Xu Liu, Xiaoyu Liu, Ling Wu, Weifeng Shi, Lu Zhang, Jie Ren, Wei Peng, Z Wang, Lei Chen

Published Jul 17, 2026• 0 citations
Publisher

Abstract

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 .

DOI
10.1016/j.physc.2026.1354910

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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 .
The nanobridge junction (NBJ) is a type of Josephson junction that is advantageous for the miniaturization of superconducting circuits. However, the current–phase relation (CPR) of the NBJ usually deviates from a sinusoidal function, which has been explained by a simplified model with correlation only to its effective length. Here, we investigated both measured and calculated CPRs of niobium NBJs of a cuboidal shape with a three-dimensional bank structure. From a sine-wave to a sawtooth-like form, we showed that deviated CPRs of NBJs can be described quantitatively by its skewness Δθ. Furthermore, the measured dependence of Δθ on the critical current I 0 from 108 NBJs turned out to be consistent with the calculated dependence derived from the change in geometric dimensions. This suggested that the CPRs of NBJs can be tuned by their geometric dimensions. In addition, the calculated scaling behavior of Δ θ versus I 0 in 3D space was provided for the future design of superconducting circuits of a high integration level by using niobium NBJs.
Josephson junction, as the core nonlinear element underpinning superconducting electronics, is characterized by its current-phase relation (CPR), which fundamentally determines the dynamical properties and functional capabilities of superconducting quantum devices. Traditional Josephson junctions typically exhibit a traditional sinusoidal CPR; however, the junctions characterized by non-sinusoidal CPR have recently attracted considerable attention due to their distinctive physical properties and promising quantum device applications. In this work, a numerical model tailored specifically for junctions exhibiting non-sinusoidal CPR is developed by integrating experimentally measured current-voltage (I-V ) characteristics from Nb/Al-AlOx/Nb junctions into a resistively and capacitively shunted junction (RCSJ) framework. By leveraging this refined model, the influence of CPR skewness on Josephson junction dynamics is systematically investigated. Our results indicate that in underdamped junctions, the critical current significantly diminishes with the increase of CPR skewness, a behavior reminiscent of the adjustable critical currents typically observed in DC superconducting quantum interference devices (SQUIDs). Conversely, in overdamped junctions, the influence of CPR skewness on the I-V characteristics is found to be negligible. However, our numerical simulations under microwave irradiation indicate that nonsinusoidal CPRs readily promote the emergence of half-integer Shapiro steps in overdamped junctions, thereby establishing CPR skewness as a plausible microscopic origin for this phenomenon. In addition, the advanced design system (ADS) simulations is employed to model nonlinear resonators and DC SQUID circuits, offering a detailed investigation into how nonsinusoidal CPRs modulate the Josephson inductance and magnetic flux response. Our findings reveal that engineering the CPR of Josephson junctions provides substantial flexibility in the design of superconducting qubits, parametric amplifiers, and non-magnetic nonreciprocal devices. This tunability underscores significant opportunities for developing next-generation superconducting electronic components. The Josephson junctions with engineered CPR offer expanded functionality for superconducting quantum technologies. This study suggests that customized CPR can enhance control over the dynamical behavior of junctions, and promote the optimized designs of superconducting qubits, parametric amplifiers, and nonmagnetic nonreciprocal devices.
High Resolution Image Download MS PowerPoint Slide Planar Josephson junctions (JJs) based on InSb nanoflags have recently emerged as an intriguing platform in superconducting electronics. The knowledge of the current-phase relationship (CPR) of such hybrid junctions is crucial for their applications. This letter presents the fabrication and investigation of superconducting quantum interference devices (SQUIDs) employing InSb nanoflag JJs. The observed features are well reproduced through numerical simulations. By measuring interference patterns in both symmetric and asymmetric SQUID configurations, we extract unprecedented details of the junctions’ CPRs. Our results demonstrate the skewness of the CPR, showing significant contributions from higher harmonics. We explore the magnetic field response of the devices across a wide range of fields (±30 mT). Finally, we assess the flux-to-voltage sensitivity of the SQUIDs to evaluate their performance as magnetometers, identifying a magnetic flux noise of S Φ 1 / 2 = 4.4 × 1 0 − 6 ⁡ Φ 0 / √ H z . These results showcase potential applications in nanoscale magnetometry.
Abstract Superconducting quantum interference devices (SQUIDs) with 3D nano-bridge junctions can be miniaturized into nano-SQUIDs that are able to sense a few spins in a large magnetic field. Among all device parameters, the inductance is key to the performance of SQUIDs with 3D nano-bridge junctions. Here, we measured the critical-current magnetic flux modulation curves of 12 devices with three design types using a current strip-line directly coupled to the SQUID loop. A best flux modulation depth of 71% was achieved for our 3D Nb SQUID. From the modulation curves, we extracted the inductance values of the current stripe-line in each design and compared them with the corresponding simulation results of InductEX. In this way, London penetration depths of 110 and 420 nm were determined for our Nb (niobium) and NbN (niobium nitride) films, respectively. Furthermore, we showed that inductances of 11 and 119 pH for Nb and NbN 3D nano-bridge junctions, respectively, dominated the total inductance of our SQUID loops which are 23 pH for Nb and 255 pH for NbN. A screening parameter being equal to one suggests optimal critical currents of 89.6 and 8.1 μ A for Nb and NbN SQUIDs, respectively. Additionally, intrinsic flux noise of 110 ± 40 n Φ 0 /(Hz) 1/2 is calculated for the Nb SQUIDs with 3D nano-bridge junctions by Langevin simulation.
A superconducting quantum interference device (SQUID) miniaturized into the nanoscale is promising in the inductive detection of a single electron spin. A nano-SQUID with a strong spin coupling coefficient, a low flux noise, and a wide working magnetic field range is highly desired in a single spin resonance measurement. Nano-SQUIDs with Dayem bridge junctions excel in a high working field range and in the direct coupling from spins to the bridge. However, the common planar structure of nano-SQUIDs is known for problems such as a shallow flux modulation depth and a troublesome hysteresis in current–voltage curves. Here, we developed a fabrication process for creating three-dimensional (3-D) niobium (Nb) nano-SQUIDs with nanobridge junctions that can be tuned independently. Characterization of the device shows up to 45.9% modulation depth with a reversible current–voltage curve. Owning to the large modulation depth, the measured flux noise is as low as 0.34 μΦ 0 /Hz 1/2 . The working field range of the SQUID is greater than 0.5 T parallel to the SQUID plane. We believe that 3-D Nb nano-SQUIDs provide a promising step toward effective single-spin inductive detection.
An analytical approach that makes it possible to reconstruct the current–phase relation (CPR) in Josephson structures included in one of the arms of a two-junction superconducting quantum interference device (SQUID), where the second junction has a significantly higher critical current and a known (sinusoidal) CPR, has been developed. The developed methods of analytical and numerical studies of current–flow transformations in two-junction SQUIDs make it possible to reconstruct the CPR of a junction with a low critical current taking into account both the existence of the self-inductance of the interferometer contour and a possible asymmetry in the supply current system. The efficiency of this approach has been confirmed by the experimental study of niobium–aluminum/aluminum oxide–niobium test structures with the known CPR.