  Graphene features topological edge bands that connect the pair of Dirac
points through either sectors of the 1D Brillouin zone depending on edge
configurations (zigzag or bearded). Because of their flat dispersion,
spontaneous edge magnetisation can arise from Coulomb interaction in graphene
nanoribbons, which has caught remarkable interest. We find an anomalous Bloch
oscillation in such edge bands, in which the flat dispersion freezes electron
motion along the field direction, while the topological connection of the bands
through the bulk leads to electron oscillation in the transverse direction
between edges of different configurations on opposite sides/layers of a bilayer
ribbon. Our Hubbard-model mean-field calculation shows that this phenomenon can
be exploited for electrical switching of edge magnetisation configurations.
