Electrons in Narrow-Band Moire Graphene: Electric and Magnetic Two-Dimensional Bloch Oscillations

Bloch oscillating electrons, moving in a two-dimensional crystal under a DC electric field, are described, in a quasiclassical picture, by trajectories that wind quasiperiodically around the 2D Brillouin zone. The oscillations feature two or more discrete frequencies that depend on the field, but not on individual particle velocities, producing narrow lines in ensemble-averaged noise power spectrum. An externally applied magnetic field alters the dynamics, creating new types of Bloch oscillations that do not exist in one-dimensional solids. The conventional “electric” oscillations persist at weak B fields; above a critical B value a different dynamics sets in that combines Bloch oscillations and Larmor drift. In this “magnetic” regime particle trajectories are extended in position space and confined in momentum space, with a complex chaotic behavior arising at the transition.