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Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions

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Abstract

Transport is non-reciprocal when not only the sign, but also the absolute value of the current depends on the polarity of the applied voltage. It requires simultaneously broken inversion and time-reversal symmetries, for example, by an interplay of spin–orbit coupling and magnetic field. Hitherto, observation of nonreciprocity was tied to resistivity, and dissipationless non-reciprocal circuit elements were elusive. Here we engineer fully superconducting non-reciprocal devices based on highly transparent Josephson junctions fabricated on InAs quantum wells. We demonstrate supercurrent rectification far below the transition temperature. By measuring Josephson inductance, we can link the non-reciprocal supercurrent to an asymmetry of the current–phase relation, and directly derive the supercurrent magnetochiral anisotropy coefficient. A semiquantitative model explains well the main features of our experimental data. Non-reciprocal Josephson junctions have the potential to become for superconducting circuits what pn junctions are for traditional electronics, enabling new non-dissipative circuit elements.

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Fig. 1: Josephson junction array and anomalous CPR.
Fig. 2: Supercurrent anisotropy and rectification.
Fig. 3: Supercurrent interference.
Fig. 4: Magnetochiral anisotropy in the fluctuation regime.

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Data availability

The data that support the findings of this study are available at the online depository EPUB of the University of Regensburg, with the identifier doi:10.5283/epub.44877. Source data are provided with this paper.

Code availability

The computer codes that support the theoretical results, the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank L. Tosi, A. Levi-Yeyati and S.H. Park for fruitful discussions. A.C. thanks M. Barth for valuable discussions on KWANT’s functionalities. C.B., L.F., A.C., S.R., P.E. F.J., D.K., J.F., N.P. and C.S. acknowledge funding by the Deutsche Forschungsgemeinschaft (German Research Foundation), Project-ID 314695032—SFB 1277 (Subprojects B05, B07 and B08). A.C., P.E.F.Jr., D.K. and J.F. also benefited from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 881603 (Graphene Flagship Core 3). A.C. and J.F. also acknowledge support from the DFG Project 454646522. Work completed by S.G., G.C.G., T.L. and M.J.M. is supported by Microsoft Quantum.

Author information

Author notes

  1. These authors contributed equally: Christian Baumgartner, Lorenz Fuchs.

Authors and Affiliations

  1. Institut für Experimentelle und Angewandte Physik, University of Regensburg, Regensburg, Germany

    Christian Baumgartner, Lorenz Fuchs, Simon Reinhardt, Nicola Paradiso & Christoph Strunk

  2. Institut für Theoretische Physik, University of Regensburg, Regensburg, Germany

    Andreas Costa, Paulo E. Faria Junior, Denis Kochan & Jaroslav Fabian

  3. Microsoft Quantum Purdue, Purdue University, West Lafayette, IN, USA

    Sergei Gronin, Geoffrey C. Gardner & Michael J. Manfra

  4. Birck Nanotechnology Center, Purdue University, West Lafayette, IN, USA

    Sergei Gronin, Geoffrey C. Gardner, Tyler Lindemann & Michael J. Manfra

  5. Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA

    Tyler Lindemann & Michael J. Manfra

  6. School of Materials Engineering, Purdue University, West Lafayette, IN, USA

    Michael J. Manfra

  7. School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA

    Michael J. Manfra

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  1. Christian Baumgartner
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Contributions

C.B. fabricated the devices and performed the measurements. L.F. and S.R. developed and optimized the measurement method. T.L., S.G. and G.C.G. designed the heterostructure, conducted molecular-beam epitaxy growth and performed initial characterization of the hybrid superconductor/semiconductor wafer. C.B. and N.P. analysed the data. N.P. and C.S. conceived the experiment. A.C., D.K. and J.F. formulated the theoretical model. A.C. performed KWANT simulations, P.E.F.Jr. conducted the k ⋅ p calculations, C.S., J.F. and M.J.M. supervised research activities at Regensburg and Purdue, respectively. All authors contributed to discussions and to the writing of the paper.

Corresponding author

Correspondence to Nicola Paradiso.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks Francesco Giazotto and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Fraunhofer patterns with in-plane magnetic fields of opposite polarity.

a, Fraunhofer patterns for the Josephson junction array, measured at Bx = 0 for selected values of By < 0. Compared to the patterns in Fig. 3b (here reproduced for ease of comparison in panel b), the By values are equal and opposite. Data in the two panels are not symmetric upon inversion of the current direction. Instead, each data set is mapped into the other. The system is thus symmetric upon simultaneous inversion of current and in-plane magnetic field direction. Interestingly, all the Fraunhofer patterns here reported are symmetric upon inversion of Bz. This demonstrates that the diode effect is not due to non-homogeneous supercurrent density nor to an asymmetric SQUID effect46,47,48.

Source data

Extended Data Fig. 2 Higher harmonics in CPR and supercurrent diode effect.

a, Computed CPR for a short rectangular junction in the presence of selected value of the out-of-plane field Bz. The CPR at Bz = 0 is that described by the Beenakker-Furusaki equation with the parameters characterized in Ref. 13. b, Modulus of the first seven Fourier sine (bn) and cosine (an) coefficients for the Bz = 0 CPR. c, Out-of-plane magnetic field dependence of the modulus of the first three sine coefficients. d, Absolute value of the difference between the measured critical currents in the two direction for By = 75 mT (black symbols). Data are normalized to the value at Bz = 0. The graph refers to the same data as in Fig. 3d. The experimental values are in good approximation described by the product of the critical current Ic and the modulus of the second Fourier coefficient ∣b2∣ (red line), both computed as a function of Bz. The former factor describes the magnitude of the critical current as a whole, while the latter quantifies how skewed the CPR is, and therefore the strength of the diode effect. Notice that the product Ic∣b2∣ makes clear why the measured critical current difference goes to zero (i) for multiples of half flux quanta Φ0/2 and (ii) with (alternately) cusp-like and parabolic-like minima.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–13 and Discussion.

Source data

Source Data Fig. 1

ASCII data for the graphs in panels d–g of Fig. 1.

Source Data Fig. 2

ASCII data for the graphs in panels a–d of Fig. 2.

Source Data Fig. 3

ASCII data for the graphs in panels a–f of Fig. 3.

Source Data Fig. 4

ASCII data for the graphs in panels a–c of Fig. 4.

Source Data Extended Data Fig. 1

ASCII data for the graphs in panel a of Extended Data Fig. 1.

Source Data Extended Data Fig. 2

ASCII data for the graphs in panels a–d of Extended Data Fig. 2.

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Baumgartner, C., Fuchs, L., Costa, A. et al. Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions. Nat. Nanotechnol. 17, 39–44 (2022). https://doi.org/10.1038/s41565-021-01009-9

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