A self-pumping mechanical analogue of Aubry-André-Harper model

We present a mechanical analogue of the Aubry-André-Harper (AAH) model where adiabatic pumping can be triggered by the signal in a non-reciprocal way. This structure consists of a one-dimensional lattice with a bulk zero energy mode which is parametrized by an angle. Depending on the value of this angle, this system supports finite frequency edge modes as a consequence of non-zero Chern numbers of the bulk bands. Interestingly, due to interaction between these finite frequency edge modes and the bulk zero mode, we find a "self-pumping effect" meaning that excitation from the end with the edge mode excites the bulk zero mode which in turn transports (pumps) the excitation from that side to the other side of the system, leading to non-reciprocity.