Active topolectrical circuits

Originally discovered in condensed-matter physics, topological protection has become a unifying paradigm for understanding robust localized wave propagation in electronic, optical, acoustic, and even geophysical systems. The excitation of topologically protected waves in passive matter typically requires external forcing in a specific frequency range. Here, we show both theoretically and experimentally that robust topological edge modes can be spontaneously self-excited in active systems made from internally powered subunits. Presenting different realizations of active nonlinear electronic circuits, we demonstrate the emergence of self-organized topological wave patterns, in close agreement with predictions from a generic mathematical model. More broadly, these results can provide guidance for designing autonomous active systems with topologically protected signaling and transmission properties.