Diffraction in Twisted Bilayer Graphene

In twisted bilayer graphene (TBG), spatial variations in the twist angle produce variations in the local electron velocity, which produces diffraction of electrons that resembles the diffraction of light in an optical medium. We follow this analogy to investigate the creation of an "electron lens" using patterning of the twist angle in TBG. We show theoretically that electron diffraction in TBG is governed by a modified Snell's law, and we use theoretical analysis and numerical simulations to explore the implications of this modified Snell's law for designing an ideal lens and for focusing of electrons by a circular lens. Interestingly, a circular lens for electrons in TBG acts similar to the usual optical version, except that the optical axis and focal point are not horizontally symmetric, and are shifted away from the line of bilateral symmetry.