Direct and diffuse reflection of electron waves at armchair edges of epitaxial graphene

Scanning tunneling microscopy (STM) is adopted to characterize the commonly formed armchair edge structure of epitaxial graphene prepared by thermal decomposition of 6H-SiC. At the smooth armchair edges, √3 × √3 patterns are usually observed as a result of quantum interference (QI) of the incident and directly reflected Bloch waves of electrons at the Fermi level and, the distinct morphologies, such as, dumbbell- and horseshoes-shaped ones can be ascribed to the phase shift of the reflected Bloch wave. However, atomically-resolved graphene lattice instead of QI patterns is imaged near the ridged armchair edges. On the analogy of light interference, when the electron waves encounter such a "rough" edge, diffuse reflection occurs and coherent conditions between the incident and reflected waves cannot be satisfied and so no QI pattern is observed. This provides a unified model describing the electronic states on graphene edges and facilitates optimal design of graphene-based electronics.