Observation of Multiple Topological edge States in Square-Root electric circuits

Abstract

Square-root topological states are new topological phases, whose intriguing topological properties are inherited from the parent lattice Hamiltonian. Because of the square-root procedure, the bulk gap of the parent Hamiltonian is doubled. In this letter, we report the observation of the square-root topological insulators (SRTIs) in topological LC circuits, whose squared Hamiltonian includes a Su-Schrieffer-Heeger (SSH) model, a well-known example of topological insulators (TI). The multiple localized edge states falling in different bandgaps are observed with characteristic phase structures, in sharp contrast to the discrete diffraction in a topologically trivial structure. These edge states with zero energy are manifested by a prominent impedance peak at the midgap frequency and directly observed by impedance measurements. Our work opens up an alternative gateway towards actively controllable topological systems and may bring about new possibilities in topology-driven electronic devices.