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Superconductor Science and Technology

Direct observations of π-leaps of superconducting phase differences in π-junction-based SQUIDs

Yuto Takeshita, Feng Li, Masayuki Higashi, Masamitsu Tanaka, Taro Yamashita, Akira Fujimaki

Published Jan 16, 2023• 10 citations
Publisher

Abstract

Abstract We directly observed π-leaps of superconducting phase differences in π-junction-based superconducting quantum interference devices (SQUIDs). The SQUIDs studied here are formed by introducing a π-junction to a conventional-junction (0-junction)-based direct current (DC)-SQUID, which is referred to as the 0-0-π SQUID. Either clockwise or counter-clockwise-circulating currents flow spontaneously in the 0-0-π SQUID because of a π-phase shift of the π-junction. In other words, the 0-0-π SQUID has a bistable state corresponding to the directions of circulating currents. π-leaps are generated by transiting between the two states of the bistable state. π-leaps are an ultra-fast phenomenon and are difficult to observe as they are. We prepared a half-flux quantum (HFQ)-SQUID that comprised two 0-0-π SQUIDs. π-leaps are reflected in a static characteristic, that is, a modulation pattern of the critical current in the HFQ-SQUID. We formed π-junctions with the PdNi layer on 0-junction-based circuits supplied by the National Institute of Advanced Industrial Science and Technology. The modulation pattern of the HFQ-SQUID had a period corresponding to π-leaps as expected, although some microstructures were observed. We demonstrated that the microstructures originated from the asymmetry inside each 0-0-π SQUID by analyzing the relationship between the phase change of 0-0-π SQUIDs and the modulation patterns.

DOI
10.1088/1361-6668/acb38d

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Abstract We directly observed π-leaps of superconducting phase differences in π-junction-based superconducting quantum interference devices (SQUIDs). The SQUIDs studied here are formed by introducing a π-junction to a conventional-junction (0-junction)-based direct current (DC)-SQUID, which is referred to as the 0-0-π SQUID. Either clockwise or counter-clockwise-circulating currents flow spontaneously in the 0-0-π SQUID because of a π-phase shift of the π-junction. In other words, the 0-0-π SQUID has a bistable state corresponding to the directions of circulating currents. π-leaps are generated by transiting between the two states of the bistable state. π-leaps are an ultra-fast phenomenon and are difficult to observe as they are. We prepared a half-flux quantum (HFQ)-SQUID that comprised two 0-0-π SQUIDs. π-leaps are reflected in a static characteristic, that is, a modulation pattern of the critical current in the HFQ-SQUID. We formed π-junctions with the PdNi layer on 0-junction-based circuits supplied by the National Institute of Advanced Industrial Science and Technology. The modulation pattern of the HFQ-SQUID had a period corresponding to π-leaps as expected, although some microstructures were observed. We demonstrated that the microstructures originated from the asymmetry inside each 0-0-π SQUID by analyzing the relationship between the phase change of 0-0-π SQUIDs and the modulation patterns.
We adopt superconductor/ferromagnet/insulator/superconductor (SFIS) Josephson junctions (JJs) as both switching JJs and intrinsic π phase shifters in superconductor digital circuits. The critical current density (Jc) and characteristic voltage (Vc) of the SFIS junctions are about 22 A/cm2 and 22 μV, respectively. The intrinsic π phase shift is confirmed by measuring the suppressed nominal critical current Icn and half-period-shifted modulation pattern of a π–π–π superconducting quantum interference device (SQUID) that contains three π-JJs in a superconducting loop. A single-flux-quantum (SFQ) circuit composed of a DC/SFQ, Josephson transmission line (JTL), and SFQ/DC converter based on SFIS JJs alone is demonstrated at 4.2 K. The energy dissipation of the SFQ/DC converter decreases by 80% because some JJs are self-biased by the π phase shifter. The intrinsic circulating currents induced by the π phase shifters lead to a narrow bias margin (±5%) and even error function, which can be solved by parameters optimization or circuit initialization in the future. The half-modulation period (Φ0/2) of a half-flux-quantum (HFQ) SQUID (a partial HFQ JTL) exhibits propagation of HFQ between π–π–π SQUIDs, indicating that more complex HFQ circuits can be developed with π-JJs alone in the future.
This study shows that we can obtain an enhanced mutual coupling by using a superconducting quantum interference device (SQUID) containing a π-phase shift Josephson junction (π-junction). The π-junction can increase the current flowing in the loop inductance of the SQUID, thereby enhancing the magnetic flux generated in the inductance. Therefore, the effective self-inductance of the SQUID can increase, resulting in an increase in the mutual coupling. We use a 0-π SQUID formed by a conventional Josephson junction (0-junction) and a π-junction. Our numerical analysis for a simplified structure revealed that the ratio of effective to original self-inductance increased to 50. To confirm this, we measured the modulation patterns of critical current in dc-SQUIDs in which part of the loop inductance was replaced with a series of 0-π SQUIDs. The observed modulation pattern revealed that the effective self-inductance became more than 10-fold larger than the original self-inductance under the conditions that the applied current is a few μA while the critical current of the 0-junction in 0-π SQUIDs is 35 μA.
We report on low-power operation of the half-flux-quantum (HFQ) shift-register circuit. We used a superconducting quantum interference device composed of two conventional switching junctions (0-junctions) and one π-shifted non-switching magnetic Josephson junction (π-junction) as a switching element, called 0-0-π SQUID. Because the π-shift assists switching by inducing a spontaneous current, the 0-0-π SQUID shows a nominal small critical current value and is easily switched by a weak driving force. This feature allows us to significantly reduce static and dynamic power consumption at junctions and bias-feeding resistors. We carefully designed the HFQ circuit elements using a circuit parameter optimization tool and introducing additional non-switching 0-0-π SQUIDs to compensate for superconductor phase shifts. We fabricated the test circuit of the 4-bit shift-register by forming Nb/PdNi/Nb π-junctions on the Nb four-layer, 10-kA/cm2 device. We successfully obtained correct operation with measured power consumption of 0.12-0.18 μW/bit, which was about 1/10 of the conventional single-flux-quantum shift-register designed with the 0-junctions of the same critical currents and the standard bias voltage.
We report a hybrid fabrication process for superconductor large-scale integrated circuits (ICs) with ferromagnetic π-shifted Josephson junctions (π junctions) and conventional 0 junctions. π junctions have a Nb/PdNi/Nb sandwich structure and are formed on the reliable Nb four-layer structure used for Nb/AlOx/Nb 0-junction-based ICs. The additional process for making π junctions causes little damage to the 0 junctions. The π phase shift for the superconducting macroscopic wave function is confirmed by forming 0-0-π SQUIDs that have two 0 junctions and one π junction in a superconducting loop. The π junction serves as the π phase shifter because the critical currents of the π junctions are much larger than those of the 0 junctions. The modulation patterns of the 0-0-π SQUIDs show a clear shift by the magnetic field corresponding to the half flux quantum (HFQ). The critical currents of the 0-0-π SQUIDs without fields, which are referred to as the nominal critical currents, are reduced depending on the product of the loop inductance and the critical current of the 0 junction. The nominal critical current reaches 1/5 of the critical current of the single 0 junction. The small values of the nominal critical currents contribute to the reduction of the power consumption in the HFQ circuit directly.
A controllable \ensuremath{\pi}-SQUID is a DC SQUID (direct-current superconducting quantum interference device) with two controllable \ensuremath{\pi} junctions as weak links. A controllable \ensuremath{\pi} junction consists of a superconducting--normal metal--superconducting Josephson junction with two additional contacts to the normal region of the junction. By applying a voltage Vc{V}_{c}Vc​ over these contacts it is possible to control the state of the junction, i.e., a conventional (0) state or a \ensuremath{\pi} state, depending on the magnitude of Vc.{V}_{c}.Vc​. We demonstrate experimentally that, by putting one junction into a \ensuremath{\pi} state, a screening current is generated around the SQUID loop at an integer external flux. To be able to do this, we have fabricated controllable $\ensuremath{\pi}$ junctions, based on Cu-Nb or Ag-Nb, in a new geometry. We show that at 1.4 K only the Ag-Nb device shows the transition to a \ensuremath{\pi} state as a function of Vc{V}_{c}Vc​ consistent with theoretical predictions. In a controllable \ensuremath{\pi}-SQUID based on Nb-Ag we observe, apart from a screening current at integer external flux, a phase shift of \ensuremath{\pi} of the ${V}_{\mathrm{SQUID}}\ensuremath{-}B$ oscillations under a suitable current bias, depending on the magnitude of Vc.{V}_{c}.Vc​.
The predominantly dx2−y2-pairing symmetry in most high-Tc superconductors provides the opportunity to fabricate Josephson junction circuits in which part of the junctions are biased by a phase difference of the superconducting order parameter of π. We present fabrication and measurements of an all high-Tc dc superconducting quantum interference device (dc SQUID) realized with thin-film technology, of which the Josephson junctions consist of one standard junction and one junction with a π-phase shift. The characteristics of the π-SQUID are compared with the properties of a standard high-Tc SQUID.