Steering and collimation of electron beams in graphene by a phased array

Abstract

We theoretically demonstrate that a set of laterally arranged p–n barriers in a graphene sample, with heights modulated by a linear potential, can act as an electronic phased array. The phase accumulated by electrons as they traverse each barrier produces a progressive phase shift between adjacent emitters, enabling control of the emission angle of the resulting beam. By combining an analytical model based on the massless Dirac equation with numerical quantum-transport simulations, we identify the condition for maximum intensity and derive the relationship between the emission angle, the potential gradient, and the carrier energy. The device operates coherently and allows continuous steering or collimation of the electron beam by tuning the electrostatic profile.