Linear response of doped graphene sheets to vector potentials

A two-dimensional gas of massless Dirac fermions (MDFs) is a very useful model to describe low-energy electrons in monolayer graphene. Because the MDF current operator is directly proportional to the (sublattice) pseudospin operator, the MDF current-current response function, which describes the response to a vector potential, happens to coincide with the pseudospin-pseudospin response function. In this work we present analytical results for the wavevector- and frequency-dependent longitudinal and transverse pseudospin-pseudospin response functions of noninteracting MDFs. The transverse response in the static limit is then used to calculate the noninteracting orbital magnetic susceptibility. These results are a starting point for the construction of approximate pseudospin-pseudospin response functions that would take into account electron-electron interactions (for example at the random-phase-approximation level). They also constitute a very useful input for future applications of current-density-functional theory to graphene sheets subjected to time- and spatially-varying vector potentials.