Measurable Lattice Effects on the Charge and Magnetic Response in Graphene

The simplest tight-binding model is used to study lattice effects on two properties of doped graphene: (i) magnetic orbital susceptibility and (ii) regular Friedel oscillations, both suppressed in the usual Dirac cone approximation. (i) An exact expression for the tight-binding magnetic susceptibility is obtained, leading to orbital paramagnetism in graphene for a wide range of doping levels which is relevant when compared with other contributions. (ii) Friedel oscillations in the coarse-grained charge response are considered numerically and analytically and an explicit expression for the response to lowest order in lattice effects is presented, showing the restoration of regular 2d behavior, but with strong sixfold anisotropy.