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. Building blocks that consist of capacitors, inductors and resistors can be used to create circuit designs that can implement the spin–orbit interaction, topological Chern state and non-Abelian Aharonov–Bohm effect.