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Physical review. B./Physical review. B

Shapiro response of superconducting diode effect derived from Andreev molecules

Sadashige Matsuo, Russell Deacon, Shohei Kobayashi, Yosuke Sato, Tomohiro Yokoyama, Tyler Lindemann, Sergei Gronin, G. C. Gardner, Koji Ishibashi, Michael J. Manfra, Seigo Tarucha

Published Mar 12, 2025• 5 citations
Publisher

Abstract

The superconducting diode effect (SDE) is a phenomenon that has attracted significant attention for its potential to establish new Josephson junction (JJ) physics and its application as a rectifier in Josephson circuits. While many experimental platforms for SDE have been reported, only a few demonstrate high efficiency. One promising system is a JJ coherently coupled with a second JJ embedded in a superconducting loop, where SDE is controllable in direction via the phase difference. Here we study SDE in such devices under microwave irradiation. With the appearance of Shapiro steps, SDE efficiency increases as the microwave power is raised. Additionally, a finite voltage difference appears without any direct bias current at high microwave powers. These results are explained by the dynamics of the JJ's washboard potential, which are common to all SDE systems. Our findings enhance the understanding of SDE dynamics and expand their potential applications.

DOI
10.1103/physrevb.111.094512

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The superconducting diode effect (SDE) is a phenomenon that has attracted significant attention for its potential to establish new Josephson junction (JJ) physics and its application as a rectifier in Josephson circuits. While many experimental platforms for SDE have been reported, only a few demonstrate high efficiency. One promising system is a JJ coherently coupled with a second JJ embedded in a superconducting loop, where SDE is controllable in direction via the phase difference. Here we study SDE in such devices under microwave irradiation. With the appearance of Shapiro steps, SDE efficiency increases as the microwave power is raised. Additionally, a finite voltage difference appears without any direct bias current at high microwave powers. These results are explained by the dynamics of the JJ's washboard potential, which are common to all SDE systems. Our findings enhance the understanding of SDE dynamics and expand their potential applications.
A Josephson junction (JJ) is a key device for developing superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. When two JJs sharing one superconducting electrode are coherently coupled and form the Andreev molecules, a supercurrent of one JJ is expected to be nonlocally controlled by the phase difference of another JJ. Here, we evaluate the supercurrent in one of the coupled two JJs as a function of local and nonlocal phase differences. Consequently, the results exhibit that the nonlocal phase control generates a finite supercurrent even when the local phase difference is zero. In addition, an offset of the local phase difference giving the JJ ground state depends on the nonlocal phase difference. These features demonstrate the anomalous Josephson effect realized by the nonlocal phase control. Our results provide a useful concept for engineering superconducting devices such as phase batteries and dissipationless rectifiers.
High Resolution Image Download MS PowerPoint Slide We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current–phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ 0 -junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.
We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ${\ensuremath{\omega}}_{\mathrm{mw}}$. With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of $e{\ensuremath{\omega}}_{\mathrm{mw}}/\ensuremath{\pi}$ in the current-voltage $(I\text{\ensuremath{-}}V)$ characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the $I\text{\ensuremath{-}}V$ characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.
We report an experimental and theoretical study of the phase diffusion in small Josephson junctions under microwave irradiation. A peculiar enhancement of the phase diffusion by microwaves is observed. The enhancement manifests itself by a pronounced current peak in the current-voltage characteristics. The voltage position V(top) of the peak increases with the power P of microwave radiation as V(top) proportional to sqrt[P], while its current amplitude weakly decreases with P. As the microwave frequency increases, the peak feature evolves into Shapiro steps with a finite slope. Our theoretical analysis, taking into account the enhancement of incoherent superconducting current by multiphoton absorption, is in good agreement with experimental data.
A high temperature superconducting YBa2Cu3Oy array of five Josephson junctions designed with additional coupling lines has been developed to demonstrate the effects of frequency locking and impedance matching for applications such as oscillators, mixers, and detectors. The Josephson self-radiation power was directly detected by a superheterodyne receiver, and Shapiro steps were also measured. The Josephson self-radiation properties reveal good quality of phase locking and microwave coupling with external circuits. The maximum self-radiation power of our array is about 50 pW which is several ten times higher than that of a single Josephson junction, and its peak point exactly satisfies the Josephson current-voltage relation. The Shapiro-step measurements show that the behavior of current-voltage curve depends on the effective inductance of coupling lines which affects the total impedance of Josephson junction array and microwave coupling. The Josephson oscillation frequency was obtained up to about 880 GHz which is 73% of the maximum available frequency calculated from the characteristic voltage of the Josephson junctions. Experimental results show that this type of Josephson junction array can improve the Josephson self-radiation power and increase the maximum detectable frequency.