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.
This is a preview of subscription content, access via your institution
Open Access articles citing this article.
Communications Physics Open Access 13 September 2022
Nature Physics Open Access 15 August 2022
Nature Communications Open Access 23 July 2022
Subscribe to Nature+
Get immediate online access to Nature and 55 other Nature journal
Subscribe to Journal
Get full journal access for 1 year
only $9.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
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.
Scaff, J. H. & Ohl, R. S. Development of silicon crystal rectifiers for microwave radar receivers. Bell Syst. Tech. J. 26, 1–30 (1947).
Shockley, W. The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Syst. Tech. J. 28, 435–489 (1949).
Onsager, L. Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405–426 (1931).
Kubo, R. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn 12, 570–586 (1957).
Tokura, Y. & Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).
Hoshino, S., Wakatsuki, R., Hamamoto, K. & Nagaosa, N. Nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors. Phys. Rev. B 98, 054510 (2018).
Rikken, G. L. J. A., Fölling, J. & Wyder, P. Electrical magnetochiral anisotropy. Phys. Rev. Lett. 87, 236602 (2001).
Rikken, G. L. J. A. & Wyder, P. Magnetoelectric anisotropy in diffusive transport. Phys. Rev. Lett. 94, 016601 (2005).
Wakatsuki, R. et al. Nonreciprocal charge transport in noncentrosymmetric superconductors. Sci. Adv. 3, e1602390 (2017).
Itahashi, Y. M. et al. Nonreciprocal transport in gate-induced polar superconductor SrTiO3. Sci. Adv. 6, eaay9120 (2020).
Fulton, T. A., Dunkleberger, L. N. & Dynes, R. C. Quantum interference properties of double Josephson junctions. Phys. Rev. B 6, 855–875 (1972).
Barone, A. & Paterno, G. Physics and Applications of the Josephson Effect 2nd edn (John Wiley and Sons, Inc., 1982)
Baumgartner, C. et al. Josephson inductance as a probe for highly ballistic semiconductor-superconductor weak links. Phys. Rev. Lett. 126, 037001 (2021).
Bezuglyi, E. V., Rozhavsky, A. S., Vagner, I. D. & Wyder, P. Combined effect of Zeeman splitting and spin-orbit interaction on the Josephson current in a superconductor-two-dimensional electron gas-superconductor structure. Phys. Rev. B 66, 052508 (2002).
Buzdin, A. Direct coupling between magnetism and superconducting current in the Josephson φ0 junction. Phys. Rev. Lett. 101, 107005 (2008).
Reynoso, A. A., Usaj, G., Balseiro, C. A., Feinberg, D. & Avignon, M. Anomalous Josephson current in junctions with spin polarizing quantum point contacts. Phys. Rev. Lett. 101, 107001 (2008).
Reynoso, A. A., Usaj, G., Balseiro, C. A., Feinberg, D. & Avignon, M. Spin-orbit-induced chirality of Andreev states in Josephson junctions. Phys. Rev. B 86, 214519 (2012).
Yokoyama, T., Eto, M. & Nazarov, Y. V. Anomalous Josephson effect induced by spin-orbit interaction and Zeeman effect in semiconductor nanowires. Phys. Rev. B 89, 195407 (2014).
Shen, K., Vignale, G. & Raimondi, R. Microscopic theory of the inverse Edelstein effect. Phys. Rev. Lett. 112, 096601 (2014).
Konschelle, F., Tokatly, I. V. & Bergeret, F. S. Theory of the spin-galvanic effect and the anomalous phase shift φ0 in superconductors and Josephson junctions with intrinsic spin-orbit coupling. Phys. Rev. B 92, 125443 (2015).
Szombati, D. B. et al. Josephson φ0-junction in nanowire quantum dots. Nat. Phys. 12, 568–572 (2016).
Assouline, A. et al. Spin-orbit induced phase-shift in Bi2Se3 Josephson junctions. Nat. Commun. 10, 126 (2019).
Mayer, W. et al. Gate controlled anomalous phase shift in Al/InAs Josephson junctions. Nat. Commun. 11, 212 (2020).
Strambini, E. et al. A Josephson phase battery. Nat. Nanotechnol. 15, 656–660 (2020).
Rasmussen, A. et al. Effects of spin-orbit coupling and spatial symmetries on the Josephson current in SNS junctions. Phys. Rev. B 93, 155406 (2016).
Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373–376 (2020).
Groth, C. W., Wimmer, M., Akhmerov, A. R. & Waintal, X. Kwant: a software package for quantum transport. New J. Phys. 16, 063065 (2014).
Mayer, W. et al. Superconducting proximity effect in InAsSb surface quantum wells with in situ Al contacts. ACS Appl. Electron. Mater. 2, 2351–2356 (2020).
Vurgaftman, I., Meyer, J. R. & Ram-Mohan, L. R. Band parameters for III-V compound semiconductors and their alloys. J. Appl. Phys. 89, 5815–5875 (2001).
Fabian, J., Matos-Abiague, A., Ertler, C., Stano, P. & Žutić, I. Semiconductor spintronics. Acta Phys. Slov. 57, 565–907 (2007).
Seraide, R. M. & Hai, G.-Q. Low-temperature electron mobility in parabolic quantum wells. Braz. J. Phys. 32, 344–346 (2002).
Suominen, H. J. et al. Anomalous Fraunhofer interference in epitaxial superconductor-semiconductor Josephson junctions. Phys. Rev. B 95, 035307 (2017).
Guiducci, S. et al. Full electrostatic control of quantum interference in an extended trenched Josephson junction. Phys. Rev. B 99, 235419 (2019).
Beenakker, C. W. J. & van Houten, H. Josephson current through a superconducting quantum point contact shorter than the coherence length. Phys. Rev. Lett. 66, 3056–3059 (1991).
Furusaki, A. & Tsukada, M. Dc Josephson effect and Andreev reflection. Solid State Commun. 78, 299–302 (1991).
Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13, 578–583 (2017).
He, P. et al. Observation of out-of-plane spin texture in a SrTiO3(111) two-dimensional electron gas. Phys. Rev. Lett. 120, 266802 (2018).
Bychkov, Y. A. & Rashba, E. I. Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. C. 17, 6039–6045 (1984).
Bychkov, Y. A. & Rashba, E. I. Properties of a 2D electron gas with lifted spectral degeneracy. J. Exp. Theor. Phys. Lett. 39, 78–81 (1984).
Dresselhaus, G. Spin-orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).
Calsaverini, R. S., Bernardes, E., Egues, J. C. & Loss, D. Intersubband-induced spin-orbit interaction in quantum wells. Phys. Rev. B 78, 155313 (2008).
Fu, J. & Egues, J. C. Spin-orbit interaction in GaAs wells: from one to two subbands. Phys. Rev. B 91, 075408 (2015).
Antipov, A. E. et al. Effects of gate-induced electric fields on semiconductor Majorana nanowires. Phys. Rev. X 8, 031041 (2018).
Mikkelsen, A. E. G., Kotetes, P., Krogstrup, P. & Flensberg, K. Hybridization at superconductor-semiconductor interfaces. Phys. Rev. X 8, 031040 (2018).
De Gennes, P. G. Superconductivity of Metals and Alloys (Addison Wesley, 1989).
Chen, C.-Z. et al. Asymmetric Josephson effect in inversion symmetry breaking topological materials. Phys. Rev. B 98, 075430 (2018).
Kononov, A. et al. One-dimensional edge transport in few-layer WTe2. Nano Lett. 20, 4228–4233 (2020).
Wang, W. et al. Evidence for an edge supercurrent in the Weyl superconductor MoTe2. Science 368, 534–537 (2020).
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.
The authors declare no competing interests.
Peer review information Nature Nanotechnology thanks Francesco Giazotto and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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.
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.
ASCII data for the graphs in panels d–g of Fig. 1.
ASCII data for the graphs in panels a–d of Fig. 2.
ASCII data for the graphs in panels a–f of Fig. 3.
ASCII data for the graphs in panels a–c of Fig. 4.
ASCII data for the graphs in panel a of Extended Data Fig. 1.
ASCII data for the graphs in panels a–d of Extended Data Fig. 2.
About this article
Cite this article
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
This article is cited by
Demonstration of a superconducting diode-with-memory, operational at zero magnetic field with switchable nonreciprocity
Nature Communications (2022)
Nature Physics (2022)
Nature Materials (2022)
Giant magnetochiral anisotropy from quantum-confined surface states of topological insulator nanowires
Nature Nanotechnology (2022)
Nature Communications (2022)