  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. 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 loop structures of
nonlinear topological bands. 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.
