  In this study, we present a mechanism of topological pumping in origami
metamaterials with spatial modulation by tuning the rotation angles. Through
coupling spatially modulated origami chains along an additional synthetic
dimension, the pumping of waves from one topological edge state to another is
achieved, where the Landau-Zener transition is demonstrated by varying the
number of coupled origami chains. Besides, the inherent nonlinearity of origami
metamaterials enable the excitation-dependent Landau-Zener tunneling
probability. Furthermore, with the increase of nonlinearity, the topological
states tend to localize in several regions in a way reminiscent of discrete
breathers. Our findings pave the way towards inter-band transitions and
associated topological pumping features in origami metamaterials.
