Misaki, K. & Nagaosa, N. Theory of the nonreciprocal Josephson effect. Phys. Rev. B 103, 245302 (2021).

Article  ADS  CAS  Google Scholar 

Hu, J., Wu, C. & Dai, X. Proposed design of a Josephson diode. Phys. Rev. Lett. 99, 067004 (2007).

Article  ADS  Google Scholar 

Chen, C.-Z. et al. Asymmetric Josephson effect in inversion symmetry breaking topological materials. Phys. Rev. B 98, 075430 (2018).

Article  ADS  CAS  Google Scholar 

Tokura, Y. & Nagaosa, N. Non-reciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).

Article  ADS  Google Scholar 

Fruchart, M., Hanai, R., Littlewood, P. B. & Vitelli, V. Non-reciprocal phase transitions. Nature 592, 363–369 (2021).

Article  ADS  CAS  Google Scholar 

Akamatsu, T. et al. A van der Waals interface that creates in-plane polarization and a spontaneous photovoltaic effect. Science 372, 68–72 (2021).

Article  ADS  CAS  Google Scholar 

Sze, S. M. & Lee, M.-K. Semiconductor Devices: Physics and Technology 3rd edn (Wiley, 2012).

Ando, F. et al. Observation of superconducting diode effect. Nature 584, 373–376 (2020).

Article  CAS  Google Scholar 

Wakatsuki, R. et al. Non-reciprocal charge transport in noncentrosymmetric superconductors. Sci. Adv. 3, e1602390 (2017).

Article  ADS  Google Scholar 

Zhang, E. et al. Nonreciprocal superconducting NbSe₂ antenna. Nat. Commun. 11, 5634 (2020).

Article  ADS  CAS  Google Scholar 

Baumgartner, C. et al. Supercurrent rectification and magnetochiral effects in symmetric Josephson junctions. Nat. Nanotechnol. 17, 39–44 (2022).

Article  ADS  CAS  Google Scholar 

Yuan, N. F. Q. & Fu, L. Supercurrent diode effect and finite momentum superconductivity. Preprint at https://arxiv.org/abs/2106.01909 (2021).

Daido, A., Ikeda, Y. & Yanase, Y. Intrinsic superconducting diode effect. Phys. Rev. Lett. 128, 037001 (2022).

Article  ADS  CAS  Google Scholar 

Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13, 578–583 (2017).

Article  CAS  Google Scholar 

Ideue, T., Koshikawa, S., Namiki, H., Sasagawa, T. & Iwasa, Y. Giant nonreciprocal magnetotransport in bulk trigonal superconductor PbTaSe₂. Phys. Rev. Res. 2, 042046(R) (2020).

Article  Google Scholar 

Wang, Y. et al. Gigantic magnetochiral anisotropy in the topological semimetal ZrTe₅. Preprint at https://arxiv.org/abs/2011.03329 (2021).

Likharev, K. K. Dynamics of Josephson Junctions and Circuits (Gordon and Breach Science Publishers, 1986).

Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 101–159 (1979).

Article  ADS  Google Scholar 

Dubos, P. et al. Josephson critical current in a long mesoscopic S-N-S junction. Phys. Rev. B 63, 064502 (2001).

Article  ADS  Google Scholar 

Golubov, A. A., Kupriyanov, M. Y. & Il’ichev, E. The current-phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).

Article  ADS  CAS  Google Scholar 

Lee, G.-H. et al. Graphene-based Josephson junction microwave bolometer. Nature 586, 42–46 (2020).

Article  ADS  CAS  Google Scholar 

Walsh, E. D. et al. Josephson junction infrared single-photon detector. Science 372, 409–412 (2021).

Article  ADS  CAS  Google Scholar 

Clarke, J. & Wilhelm, F. K. Superconducting quantum bits. Nature 453, 1031–1042 (2008).

Article  ADS  CAS  Google Scholar 

Likharev, K. K. & Semenov, V. K. RSFQ logic/memory family: a new Josephson-junction technology for sub-terahertz-clock-frequency digital systems. IEEE Trans. Appl. Supercond. 1, 3–28 (1991).

Article  ADS  Google Scholar 

Devoret, M. H. & Schoelkopf, R. J. Superconducting circuits for quantum information: an outlook. Science 339, 1169–1174 (2013).

Article  ADS  CAS  Google Scholar 

Jiang, J. et al. Exploration of new ferromagnetic, semiconducting and biocompatible Nb₃X₈ (X = Cl, Br or I) monolayers with considerable visible and infrared light absorption. Nanoscale 9, 2992–3001 (2017).

Article  CAS  Google Scholar 

Pasco, C. M., El Baggari, I., Bianco, E., Kourkoutis, L. F. & McQueen, T. M. Tunable magnetic transition to a singlet ground state in a 2D van der Waals layered trimerized Kagome magnet. ACS Nano 13, 9457–9463 (2019).

Article  CAS  Google Scholar 

Yoon, J. et al. Anomalous thickness-dependent electrical conductivity in van der Waals layered transition metal halide, Nb₃Cl₈. J. Phys. Condens. Matter 32, 304004 (2020).

Article  CAS  Google Scholar 

Haraguchi, Y. et al. Magnetic-nonmagnetic phase transition with interlayer charge disproportionation of Nb₃ trimers in the cluster compound Nb₃Cl₈. Inorg. Chem. 56, 3483–3488 (2017).

Article  CAS  Google Scholar 

Sheckelton, J. P., Plumb, K. W., Trump, B. A., Broholm, C. L. & McQueen, T. M. Rearrangement of van der Waals stacking and formation of a singlet state at T = 90 K in a cluster magnet. Inorg. Chem. Front. 4, 481–490 (2017).

Article  CAS  Google Scholar 

Castellanos-Gomez, A. et al. Deterministic transfer of two-dimensional materials by all-dry viscoelastic stamping. 2D Mater. 1, 011002 (2014).

Article  CAS  Google Scholar 

Xi, X. et al. Ising pairing in superconducting NbSe₂ atomic layers. Nat. Phys. 12, 139–143 (2015).

Article  Google Scholar 

Kleiner, R., Koelle, D., Ludwig, F. & Clarke, J. Superconducting quantum interference devices: state of the art and applications. Proc. IEEE 92, 1534–1548 (2004).

Article  CAS  Google Scholar 

Yabuki, N. et al. Supercurrent in van der Waals Josephson junction. Nat. Commun. 7, 10616 (2016).

Article  ADS  CAS  Google Scholar 

Kim, M. et al. Strong proximity Josephson coupling in vertically stacked NbSe₂-graphene-NbSe₂ van der Waals junctions. Nano Lett. 17, 6125–6130 (2017).

Article  ADS  CAS  Google Scholar 

Kitamura, S., Nagaosa, N. & Morimoto, T. Nonreciprocal Landau–Zener tunneling. Commun. Phys. 3, 63 (2020).

Article  Google Scholar 

Xu, Y. et al. Filling-enforced obstructed atomic insulators. Preprint at https://arxiv.org/abs/2106.10276 (2021).

Xu, Y. et al. Three-dimensional real space invariants, obstructed atomic insulators and a new principle for active catalytic sites. Preprint at https://arxiv.org/abs/2111.02433 (2021).

Song, T. et al. Giant tunneling magnetoresistance in spin-filter van der Waals heterostructures. Science 360, 1214–1218 (2018).

Article  ADS  CAS  Google Scholar 

Wang, Z. et al. Very large tunneling magnetoresistance in layered magnetic semiconductor CrI₃. Nat. Commun. 9, 2516 (2018).

Article  ADS  Google Scholar 

Krasnov, V. M., Oboznov, V. A. & Pedersen, N. F. Fluxon dynamics in long Josephson junctions in the presence of a temperature gradient or spatial nonuniformity. Phys. Rev. B 55, 14486–14498 (1997).

Article  ADS  CAS  Google Scholar 

Goldman, A. M. & Kreisman, P. J. Meissner effect and vortex penetration in Josephson junctions. Phys. Rev. 164, 544–547 (1967).

Article  ADS  Google Scholar 

Kononov, A. et al. One-dimensional edge transport in few-layer WTe₂. Nano Lett. 20, 4228–4233 (2020).

Article  ADS  CAS  Google Scholar 

Watanabe, N. et al. The shape dependency of two-dimensional magnetic field dependence of a Josephson junction. J. Appl. Phys. 103, 07C707 (2008).

Article  Google Scholar 

Vergniory, M. G. et al. A complete catalogue of high-quality topological materials. Nature 566, 480–485 (2019).

Article  ADS  CAS  Google Scholar 

Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

Article  ADS  CAS  Google Scholar