  A wide range of materials like graphene, topological insulators and
transition metal dichalcogenides (TMDs) share an interesting property: the low
energy excitations behave as Dirac particles. This emergent behavior of Dirac
quasiparticles defines a large class of media that are usually called Dirac
materials. The linear and nonlinear optical properties of Dirac materials with
a gap are still largely unexplored, and in this Letter we build the foundations
of a novel way to study the linear optical properties of these two-dimensional
media. Our approach is based on a new Dirac-like formulation of the standard
semiconductor Bloch equations used in semiconductor physics. We provide an
explicit expression of the linear absorbance -- which we call the relativistic
Elliott formula -- and use this to quantify the variation of the continuum
absorbance spectrum with the strength of the Coulomb interaction (the
Sommerfeld factor). Our calculations also show how the Coulomb enhancements
scales with the bandgap and vanishes for zero bandgap, shedding new light on
the behaviour of graphene for low light intensities. The results presented are
in good quantitative agreement with published experimental results. Our new
theory will allow researchers to explore the nonlinear interactions of intense,
ultrashort pulses with TMDs, and the framework is flexible enough to be adapted
to different experimental situations, such as cavities, multilayers,
heterostructures and microresonators.
