Edge states and topological pumping in stiffness-modulated elastic plates

We demonstrate that modulations of the stiffness properties of an elastic plate along a spatial dimension induce edge states spanning nontrivial gaps characterized by integer-valued Chern numbers. We also show that topological pumping is induced by smooth variations of the phase of the modulation profile along one spatial dimension, which results in adiabatic edge-to-edge transitions of the edge states. The concept is first illustrated numerically for sinusoidal stiffness modulations and then experimentally demonstrated in a plate with square-wave thickness profile. The presented numerical and experimental results show how continuous modulations of properties may be exploited in the quest for topological phases of matter. This opens new possibilities for topology-based waveguiding through slow modulations along a second dimension, spatial or temporal.