Journal of Experimental and Theoretical Physics Letters
Determination of the Current–Phase Relation in Josephson Junctions by Means of an Asymmetric Two-Junction SQUID
Lev V. Ginzburg, Igor E. Batov, V. V. Bol’ginov, Sergey V. Egorov, Vladimir I. Chichkov, Andrey E. Schegolev, N. V. Klenov, Igor I. Soloviev, Sergey V. Bakurskiy, M. Yu. Kupriyanov
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.
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.
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 .
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.
The signal properties of radio frequency (rf) (SQUIDs) based on YBa2Cu3O7−x symmetrical 30° and asymmetrical 45° grain-boundary Josephson junctions have been experimentally investigated. Both amplitude as well as phase detection have been used to read out the SQUID output signal. Comparison of the SQUID output signals to each other is given. It is shown that peculiarities of the rf SQUID response of SQUIDs with a 45° grain-boundary Josephson junction are consistent with an unconventional current-phase relation (CPR) of the Josephson junction, namely, the CPR contains a finite amplitude of the second harmonic.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
The development of superconducting electronics requires careful characterization of the components that makeup electronic circuits. Superconducting weak links are the building blocks of most superconducting electronic components and are characterized by highly nonlinear current-to-phase relations (CPRs), which are often not perfectly known. Recent research has found that the Josephson diode effect (JDE) can be related to the high harmonic content of the current-to-phase relation of the weak links embedded in superconducting interferometers. This makes the JDE a natural tool for exploring the harmonic content of weak links beyond single-harmonic CPR. In this study, we present the theoretical model and experimental characterization of a double-loop superconducting quantum interference device (DL-SQUID) that embeds all-metallic superconductor-normal metal-superconductor junctions. The proposed device exhibits the JDE due to the interference of the supercurrents of three weak links in parallel, and this feature can be adjusted through two magnetic fluxes, which act as experimental knobs. We carry out a theoretical study of the device in terms of the relative weight of the interferometer arms and the experimental characterization concerning flux tunability and temperature.