POSTPONED Coulomb effects in the absorption spectra of two dimensional Dirac materials

Coulomb effects in the absorption spectra of two dimensional
Dirac materials
Leone Di Mauro Villari
Condensed matter physics is witnessing a rapid expansion of materials with Dirac fermion
quasiparticle excitations. In recent works it has been shown that a full understanding of
the optical properties of such materials requires one to go beyond the standard approach
of the semiconductor Bloch equations (SBEs). In his influential paper Ishikawa derived
an extended version of the SBEs for graphene using the formalism of instantaneous
eigenstates. More recently his approach was generalised further for the case of a gapped
material. These generalised Dirac-Bloch (DBEs) equations reproduce novel and
previously unexplained nonlinear optical properties of graphene and gapped graphene,
however they do not include Coulomb interactions that are in general very strong in two
dimensional semiconductors. starting from the quantisation of the instantaneous Dirac
field we include Coulomb interactions and provide a fully renormalised version of the
DBEs. By solving these equations we account for the linear optical properties of 2D Dirac
semiconductor and derive an explicit Elliott formula for the absorption. We also discuss
the variation of the continuum absorption spectrum with the strength of the Coulomb
interaction (the Dirac-Sommerfeld factor) and how the absorption spectrum evolves as the
energy gap is reduced to zero.