Effective Hamiltonian for electron waves in artificial graphene: A first-principles derivation

We propose a first-principles effective medium formalism to study the propagation of electron waves in semiconductor heterostructures with a zero band gap. Our theory confirms that near the $K$ point the dynamics of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer. Furthermore, we highlight that even though other superlattices based on semiconductors with a zincblende-type structure can have a zero band-gap and a linear energy-momentum dispersion, the corresponding effective medium Hamiltonian is rather different from that of graphene, and can be based on a single-component wave function.