Breakdown of quantization in nonlinear Thouless pumping

Abstract The dynamics of solitons driven in a nonlinear Thouless pump and its connection with the system’s topology were recently explored for both weak and strong nonlinear strength. Using both a self-consistent algorithm and 4th order Runge Kutta method, this work uncovers the fate of nonlinear Thouless pumping in the regime of intermediate nonlinearity, thus establishing a fascinating crossover from the observation of nonzero and quantized pumping at weak nonlinearity to zero pumping at strong nonlinearity. We identify the presence of critical nonlinearity strength at which quantized pumping of solitons breaks down regardless of the protocol time scale. Such an obstruction to pumping quantization is attributed to the presence of self-crossing in nonlinear topological bands. By considering another type of pumping involving Bloch states, we further show how the presence of self-crossing bands also leads to breakdown of quantization, but in a completely different manner from that in the case of soliton pumping. Our results not only unveil a missing piece of physics in nonlinear Thouless pumping, but also provide a means to detect loop structures of nonlinear systems investigated in real space and momentum space.