Nonlinear screening of charges induced in graphene by metal contacts

To understand the band bending caused by metal contacts, we study the potential and charge density induced in graphene in response to contact with a metal strip. We find that the screening is weak by comparison with a normal metal as a consequence of the ultra-relativistic nature of the electron spectrum near the Fermi energy. The induced potential decays with the distance from the metal contact as x^{-1/2} and x^{-1} for undoped and doped graphene, respectively, breaking its spatial homogeneity. In the contact region the metal contact can give rise to the formation of a p-p, n-n, p-n junction (or with additional gating or impurity doping, even a p-n-p junction) that contributes to the overall resistance of the graphene sample, destroying its electron-hole symmetry. Using the work functions of metal-covered graphene recently calculated by Khomyakov et al. [Phys. Rev. B 79, 195425 (2009)] we predict the boundary potential and junction type for different metal contacts.