Realization in circuits of a Chern state with an arbitrary Chern number

The Chern insulator, as the most prominent topological state of matter, is characterized by the Chern number $\mathcal{C}$, which in principle can take any integer values. So far, most realizations of the Chern insulator are limited to $|\mathcal{C}|=1$, and achieving higher Chern numbers remains challenging. Here, we propose a general scheme to realize the Chern state with arbitrarily large Chern number in an electric circuit. Our proposal is based on the possibility of precise control on long-range couplings, which is a unique advantage of circuit systems. Besides simulations, we present an experimental demonstration of a $\mathcal{C}=3$ state fabricated on a printed circuit board and directly image its topological chiral edge modes via AC sweep analysis. Our work opens a horizon for exploring exotic topological states of matter in classical systems.