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Creation of sharp lateral p-n junctions in graphene devices, with transitionwidths well below the Fermi wavelength of graphene charge carriers, is vital tostudy and exploit these electronic systems for electron-optical applications.The achievement of such junctions is, however, not trivial due to the presenceof a considerable out-of-plane electric field in lateral p-n junctions,resulting in large widths. Metal-graphene interfaces represent a novel,promising and easy to implement technique to engineer such sharp lateral p-njunctions in graphene field-effect devices, in clear contrast to the much wider(i.e. smooth) junctions achieved via conventional local gating. In this work,we present a systematic and robust investigation of the electrostatic problemof metal-induced lateral p-n junctions in gated graphene devices forelectron-optics applications, systems where the width of the created junctionsis not only determined by the metal used but also depends on external factorssuch as device geometries, dielectric environment and different operationalparameters such as carrier density and temperature. Our calculationsdemonstrate that sharp junctions can be achieved via metal-graphene interfacesat room temperature in devices surrounded by dielectric media with low relativepermittivity. In addition, we show how specific details such as the separationdistance between metal and graphene and the permittivity of the gap in-betweenplays a critical role when defining the p-n junction, not only defining itswidth w but also the energy shift of graphene underneath the metal. Theseresults can be extended to any two-dimensional (2D) electronic system doped bythe presence of metal clusters and thus are relevant for understandinginterfaces between metals and other 2D materials.

Electrostatics of metal-graphene interfaces: sharp p-n junctions for electron-optical applications