Bloch oscillations of topological edge modes

Under the action of a weak constant force a wave packet in periodic potential undergoes periodic oscillations in space, returning to the initial position after one oscillation cycle. This wave phenomenon, known as Bloch oscillations (BOs), pertains to many physical systems. Can BOs also occur in topological insulators with topologically protected edge states? This question is highly nontrivial, because in topological insulators with broken time-reversal symmetry, the edge states propagate unidirectionally without backscattering, hence BOs that typically involve stages, where a wave packet moves along and against the direction of the force, seem to be impossible in such systems when force acts parallel to the edge of the insulator. Here we reveal that BOs still occur with topological edge states, but in a nonconventional way: they are accompanied not only by oscillations along the edge in the direction of force, but also by oscillations in the direction transverse to that of the force. A full BO cycle involves switching between edge states at the opposite edges through delocalized bulk modes. Bloch oscillations of the topological edge states require to scan the first Brillouin zone twice to complete one cycle, thus they have a period that is two times larger than the period of usual BOs. All these unusual properties are in contrast to BOs in nontopological systems.