Semi-classical limit of the Dirac equation in curved space and applications to strained and photonic graphene

Abstract The semi-classical regime of static Dirac matter is derived from the Dirac equation in curved space-time. The leading- and next-to-leading-order contributions to the semi-classical approximation are evaluated. While the leading-order yields classical equations of motion with relativistic Lorentz and a geometric forces related to space curvature, the next-to-leading-order gives a transport-like equation with source terms. We apply the proposed strategy to the simulation of electron propagation on strained graphene surfaces, as well as to the dynamics of edge states in photonic graphene.