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.