Circuits provide ideal platforms of topological phases and matter, yet the
study of topological circuits in the strongly nonlinear regime, has been
lacking. We propose and experimentally demonstrate strongly nonlinear
topological phases and transitions in one-dimensional electrical circuits
composed of nonlinear capacitors. Nonlinear topological interface modes arise
on domain walls of the circuit lattices, whose topological phases are
controlled by the amplitudes of nonlinear voltage waves. Experimentally
measured topological transition amplitudes are in good agreement with those
derived from nonlinear topological band theory. Our prototype paves the way
towards flexible metamaterials with amplitude-controlled rich topological
phases and is readily extendable to two and three-dimensional systems that
allow novel applications.Comment: accepted by Frontiers of Physics, 18+9 pages, 4+3 figure