Models for the electronic properties of twistronic few-layer graphenes

Abstract

In this thesis, we present the characterisation and electronic properties of aligned and twisted multilayered graphene systems, delving into their spectroscopic signatures. We begin by deriving the tight-binding Hamiltonian for graphene and expand this to the hybrid k · p tight-binding Hamiltonian to describe both aligned and twisted multilayer graphenes. We build upon these models to characterise how they react to external gating and how this influences the electronic structure of the system. Following this, we derive how to extrapolate the angle-resolved photoemission spectra (ARPES) from the eigenvalues of the previously derived Hamiltonian. This thesis will be divided into two sections; the first will deal with aligned graphene structures. After all necessary initial derivations, we will present the first original work of this thesis, a study of the spectroscopic signatures for 4-layer graphenes provided by ARPES, optical-absorption and Raman spectroscopy. We use these three techniques to study all stacking arrangements of 4- layered graphene systems to help experimentalists identify the novel mixed stacking order in 4-layered graphene, which has recently grown in popularity. The second original work expands upon the mixed stacking of 4-layered graphene to a general model for twin boundary (mixed) stacked graphenes with the potential to host ferroelectricity. These nABAm layered stacks lack inversion symmetry, allowing for an unequal distribution of charge across the layers and the necessary conditions to host this polarisation. For this system, we studied the effect of a uniform charge redistribution across the layer that accounts for the screening fields produced by this unequal charge distribution and thus reduces the net polarisation. Proceeding this section on aligned graphenes, we move to look at their twisted counterparts. Once again, we conduct all necessary derivations and then present a published work on the topic. The final published work of this thesis highlights the usefulness of ARPES in studying the band structure of few-layered graphenes but also seeks to validate the previously derived model with experimental collaboration. An additional result of this work was one of the first experimental observations of a flat band in twisted double bilayer graphene at 1.5 degrees that was validated using theoretical spectra. The overall theme of this thesis lends itself to trying to understand the spectra and novel properties of several multilayered graphene systems.

Date of Award	1 Aug 2024
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Vladimir Falko (Supervisor)