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 C, which in principle can take any integer values. So far, most realizations of the Chern insulator are limited to |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 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.