Coulomb effects in the absorbance spectra of two-dimensional Dirac materials

Abstract

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.