The theory for a 2D electron diffractometer using graphene

Electrons near the Fermi level behaving as massless Dirac fermions in graphene in (1+2)-D relativistic spacetime have been confirmed by an experiment. Using this aspect, a myriad of novel and interesting devices can be sought. In this paper, we laid out the theory for using a monolayer graphene sheet as an electron diffractometer, aiming at the determination of surface properties in materials. The key ingredient is the Mott scattering of electrons by screened Coulomb scatterers in (1+2)-D spacetime. The specific array of scatterers provided by a given surface placed in contact with a graphene sheet will induce an angular distribution for the electron scattering events, which can be properly measured through the electric current flowing to external electrodes. It can provide an in situ technique for characterizing quantum dot superlattices with a resolution of a few nanometers.