Realization of the square-root Dirac semimetal in electrical circuits

We implement the topological semimetal state generated by the square-root operation in electrical circuits. In this system, the energy bands intersect at finite energies, with the topological properties originating from the parent Hamiltonian. By designing a ribbon circuit, we observe the edge state and measure its frequency spectrum directly, the topological nature of which is characterized by the winding number. Compared to the bidirectional edge state of semimetals that cannot transmit information in a single direction, there is also considerable interest in the unidirectional edge state of Chern insulators. We show that, by introducing the next-nearest-neighbor interactions, the system transforms from a topological semimetal phase to the topological insulator phase, which supports the unidirectional edge modes. Our results show the ability of electrical circuits to realize semimetal states and set examples for other systems to study square-root topological physics.