Electronic and Optical Properties of 2D Materials

Abstract

In this thesis, we contribute to the understanding of electronic and optical properties of 2-dimensional materials, with a strong focus on graphene-based nanostructures \cite{graphene_book}. The thesis is structured into eight chapters, starting with an introduction and ending with a conclusion.

In chapter 2, we present the methods used throughout this thesis. We start by introducing the tight-binding model to understand the single-particle properties of graphene, bilayer graphene, and graphene quantum dots. We then introduce configuration interaction, the Hubbard model, the Bethe-Salpeter equation, and Hartree-Fock as tools for tackling the interacting problem and correlated electron systems. We also discuss numerical methods, including techniques for addressing the numerical complications that arise when working with the many-body problem such as the calculation of Coulomb matrix elements.

In chapter 3, we present a new approach to the energy spectra of $p_z$ electrons in small hexagonal graphene quantum dots. This approach is analytical, and allows us to predict the dependence of the energy gap on size and edge type.

In chapter 4, we describe a proposal of a quantum simulator of an extended bipartite highly tunable Hubbard model with broken sublattice symmetry inspired by graphene. We predict the electronic and magnetic properties of a small simulator. The proposed simulator, allows us to study the ground state of the Hubbard Hamiltonian for a broad range of regimes accessible due to the high tunability of the simulator.

In chapter 5, we study the electronic properties of quasi 2-dimensional quantum dots made of topological insulators using HgTe. We show that in a square HgTe quantum dot one set of material parameters defines the topologically nontrivial case, in which topologically protected edge states are found, and another set of parameters defines a topologically trivial regime corresponding to a trivial insulator without edge states.

In chapter 6, we examine excitons in AB-stacked gated bilayer graphene (BLG) quantum dots (QDs). We confine both electrons and holes using gates and demonstrate that excitons can exist in the BLG QD. We predict absorption to occur in the terahertz regime and find that low-energy excitons are dark.

In chapter 7, we determine the many-body states of massive Dirac Fermions confined in a bilayer graphene lateral gated quantum dot. Tuning the strength of Coulomb interactions versus the single-particle level spacing we predict the existence of spontaneously spin and valley symmetry-broken states of interacting massive Dirac Fermions.