  A Thouless pump can be regarded as a dynamical version of the integer quantum
Hall effect. In a finite-size configuration, such topological pump displays
edge modes that emerge dynamically from one bulk-band and dive into the
opposite bulk-band, an effect that can be reproduced with both quantum and
classical systems. Here, we report the first un-assisted dynamic energy
transfer across a metamaterial, via pumping of such topological edge modes. The
system is a topological aperiodic acoustic crystal, with a phason that can be
fast and periodically driven in adiabatic cycles. When one edge of the
metamaterial is excited in a topological forbidden range of frequencies, a
microphone placed at the other edge starts to pick up a signal as soon as the
pumping process is set in motion. In contrast, the microphone picks no signal
when the forbidden range of frequencies is non-topological.
