Ultrashort nonlinear light-matter interactions in two-dimensional quasirelativistic systems

Abstract

An encompassing study of nonlinear optical properties of two-dimensional quasirel ativistic systems is presented. The electrons in such systems may be adequately described by Dirac spinors, solutions to an equation formally equivalent to the Dirac equation in (2 + 1) dimensions. In order to model the carrier dynamics as a conse quence of optical excitations, the Dirac-Bloch Equations (DBEs) are derived, their framework explained and their predictions simulated in a wide range of excitation conditions. In particular, intense and ultrashort pulses, whose effect on media is oftentimes challenging to obtain, are used to study and analyse general optical fea tures through a prediction of the non-perturbative current and respective spectrum. As a starting point, pristine graphene samples are analysed and it is shown that the DBEs predict previously-forbidden second-harmonic generation. This result is to be contrasted with predictions from the Semiconductor Bloch Equations, which are shown to be inadequate to model graphene in such an excitation regime. If a gap in the spectrum is opened, the carriers acquire a Berry phase and may also produce interband-mediated harmonics of any desired order upon appropriate tun ing. The effects of lack of centrosymmetry, trigonal warping and spin-orbit coupling are also considered, and studied for transition metal dichalcogenides by applying the generalised Dirac-Bloch Equations. High even-harmonic generation, in accordance with recent experiments, is predicted, alongside anisotropic effects on the current. The results and methods outlined in this thesis help establish new techniques to un derstand and predict the nonlinear optical behaviour of a range of two-dimensional relativistic-like semiconductors admitting two effective bands, and help pave the way to predict quantitatively, in a generalised fashion, the effect of wide range of intrinsic or deliberate properties on nonlinear optical features of the media.