Topological Bloch oscillations

Abstract

The traditional view of Bloch oscillations is that they rely on the translational symmetry of crystals. These oscillations occur with a fundamental period ${T}_{B}$, the time it takes a semiclassical wave packet to travel across the Brillouin zone. We introduce a new type of Bloch oscillation whose period equals an integer multiple of ${T}_{B}$. The period multiplication relies on crystalline point-group symmetries, as exemplified by rotations and reflections. The integer-valued multiplier is robust against symmetric deformations of the crystal. It is the first example of a crystalline-symmetry-protected topological invariant in electric transport.