Optical Properties of Bilayer Graphene Quantum Dots

Abstract

In this thesis, we study graphene's optical and electrical properties, primarily focusing on bilayer graphene (BLG) quantum dots (QDs). We discuss a tight-binding model to accurately model the single-particle behavior of monolayer and bilayer graphene. Additionally, we introduce theoretical and numerical methods, including the many-body Hamiltonian, configuration interaction method, Bethe-Salpeter equation (BSE), and computation of Coulomb matrix elements to analyze electron-electron interactions in many-body systems.

We examine gated BLG under a perpendicular electric field, which opens a gap in the band structure. Next, lateral gates can be applied in a way that leads to the emergence of a QD that effectively confines electrons and holes. Employing an atomistic tight-binding model for millions of atoms, we compute the single-particle QD energy spectrum and dipole matrix elements (DMEs) to analyze the oscillator strengths and optical selection rules. We incorporate electron-electron interactions via microscopic Coulomb matrix elements and solve the BSE to obtain the excitonic energy spectrum. Furthermore, we obtain the excitonic absorption spectrum and predict the existence of dark low-energy exciton states.

Subsequently, we examine the effects of a shallow lateral confining potential and trigonal warping (TW) on the electronic structure of laterally gated BLG QDs. We begin by analyzing the influence of TW on the QD energy spectrum as the confining potential depth varies. We find a regime where the QD levels are dominated by the presence of three minivalleys for each K-valley. We obtain the absorption spectrum for a shallow confining potential depth, which further amplifies the effects of TW on the optical properties. Our results predict two degenerate bright exciton states, each built of the three minivalley states.

Finally, we utilize an effective mass model for BLG QDs to explain the previously observed optical selection rules, where TW effects were neglected. Labeling the QD states with a generalized angular momentum gives deeper insights into the selection rules that were not apparent in the atomistic model. Understanding interacting electrons and holes in gated BLG QDs opens potential applications in storing, detecting, and manipulating photons in the terahertz (THz) energy range.