Elecromagnetic Fileld dependendent Coulomb renormalisation in Dirac Materials

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. We discuss how the absorption spectrum evolves as the energy gap is reduced to zero. We then study the strong Coulomb coupling regime in which the excitons form a relativistic Bose-Einsten condensate.