  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 wavefunction.

Mesoscale and Nanoscale Physics