Ballistic Guided Electron States in Graphene

Guiding electronic waves in a manner similar to photon transmission in optical fibers is key for developing the electron-optics toolbox. Here we outline a `weak guiding' approach, in which efficient diffraction around disorder results in low-loss, high-finesse electron guiding. We describe an implementation of this scheme for guiding along a narrow-width line gate in gapless and gapped graphene. A simple model for weak guiding, which relies on the Jackiw-Rebbi midgap states, is introduced and solved. The weak-guiding modes are shown to exist for confining potential of either sign and no matter how strong or weak. Modes evolve in a cyclic manner upon varying gate potential, repeatedly sweeping the Dirac gap and becoming dispersionless (flat band) at certain magic values of gate potential. Large mode widths facilitate diffraction around disorder in the core region, enabling exceptionally large mean free paths and long-range ballistic propagation.