Electronic highways in bilayer graphene.

Bilayer graphene with an interlayer potential difference has an energy gap and, when the potential difference varies spatially, topologically protected one-dimensional states localized along the difference's zero lines. When disorder is absent, electronic travel directions along zero-line trajectories are fixed by valley Hall properties. Using the Landauer-Büttiker formula and the nonequilibrium Green's function technique, we demonstrate numerically that collisions between electrons traveling in opposite directions, due to either disorder or changes in path direction, are strongly suppressed. We find that extremely long mean free paths of the order of hundreds of micrometers can be expected in relatively clean samples. This finding suggests the possibility of designing low power nanoscale electronic devices in which transport paths are controlled by gates which alter the interlayer potential landscape.