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Non-Abelian gauge fields in circuit systems


Circuits can provide a platform to study novel physics and have been used, for example, to explore various topological phases. Gauge fields—particularly, non-Abelian gauge fields—can play a pivotal role in the design and modulation of novel physical states, but their circuit implementation has so far been limited. Here we show that non-Abelian gauge fields can be synthesized in circuits created from building blocks that consist of capacitors, inductors and resistors. With these building blocks, we create circuit designs for the spin–orbit interaction and the topological Chern state, which are phenomena that represent non-Abelian gauge fields in momentum space. We also use the approach to design non-reciprocal circuits that can be used to implement the non-Abelian Aharonov–Bohm effect in real space.

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Fig. 1: Building blocks for non-Abelian gauge field in the circuit.
Fig. 2: SOI circuit.
Fig. 3: Topological Chern circuit.
Fig. 4: Non-reciprocal circuit that generates a non-Abelian phase factor.
Fig. 5: Real-space non-Abelian Aharonov–Bohm effect.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

The codes that support the findings of this study are available from the corresponding authors upon reasonable request.


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We thank H. M. Weng, C. Fang, D. Zhang, H. Wang and S. Chang for valuable discussions. R.Y. acknowledges support from the National Key Research and Development Program of China (nos. 2017YFA0304700 and 2017YFA0303402), the National Natural Science Foundation of China (no. 11874048) and the Beijing National Laboratory for Condensed Matter Physics. F.S. acknowledges support from the National Natural Science Foundation of China (nos. 92161201, 12025404, 11904165 and 11904166).

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Authors and Affiliations



R.Y. supervised the project. J.W., Z.W. and R.Y. drew the circuit diagram of the SOI PCB. Z.W. and R.Y. measured the experimental data of the SOI circuit. Z.Y., Y.H. and R.Y. drew the circuit diagram of the Chern PCB. Z.W., T.W., Z.Y., Y.H. and Z.S. measured the experimental data of the Chern circuit. Z.W., Y.B., S.Z. and F.F. measured the experimental data of the non-Abelian Aharonov–Bohm effect. J.W. wrote part of the data acquisition program for the experimental instruments. F.S. and R.Y. analysed the data.

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Correspondence to Fengqi Song or Rui Yu.

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Nature Electronics thanks Biao Yang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–6, Sections 1–4 and Tables 1 and 2.

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Wu, J., Wang, Z., Biao, Y. et al. Non-Abelian gauge fields in circuit systems. Nat Electron 5, 635–642 (2022).

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