Light-matter interactions and nonlinear condensate waves in two dimensional pseudo-relativistic materials

Abstract

In this work we present a comprehensive analysis of light-matter interactions and exciton condensation in two dimensional pseudo-relativistic materials. Charge carriers in these materials can be adequately described with a condensed matter version of the Dirac equation in 2+1 dimensions. To model the dynamics of the carrier with both light-matter and Coulomb interactions, we derive a renormalised version of the Dirac-Bloch equations that have been recently introduced to describe effectively the optical properties of pseudo-relativistic quasiparticle excitations. The renormalised equation are used to study the Coulomb effects on the linear absorbance spectra of such materials. After this analysis a mean field model to describe the Bose-Einstein condensation of pseudo-relativistic excitons is derived and solved. A particular localised solution of this model is studied in different physical situations. The last part of this thesis concerns the nonlinear optical properties of bilayer graphene investigated with an appropriate extension of the Dirac-Bloch equations. Details are given on the generation of odd harmonics and on their relation with the electronic quasiparticle spectrum.