Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Physics

Supervisor(s)

Dr. Michael G. Cottam

Abstract

The discovery of graphene - a 2D material with superior physical properties - in 2004 was important for the intensive global research to find alternatives to three-dimensional (3D) semiconductor materials in industry. At the same time there have been exciting advances for 2D magnetic materials on the nanometer scale. The superior properties of graphene are mainly attributed to its crystal structure and its relatively short-range interactions. These properties show that natural and artificial 2D materials are promising for new applications.

In this thesis we have carried out a comprehensive investigation of the effects of the 2D lattice structures, the roles of nearest neighbor (NN) and next nearest neighbor (NNN) interactions and the formation of coupled bilayer systems in both the electronic and the magnetic geometries (chosen specifically to be nano-ribbons or stripes). In the case of honeycomb lattices (which occur in graphene and can be produced artificially by growing nanodot arrays for ferromagnetic structures) the effects of different edges of the zigzag and armchair types are studied with emphasis on the localized modes that may occur. Impurity sites in the form of one or more lines of impurities introduced substitutionally are considered from the perspectives that they give additional localized mode effects and they change the spatial quantization (for example, as studied via the density of states for the modes). The theoretical methods employed throughout the thesis are based on the second quantization forms of both the tight-binding Hamiltonian for electronic excitations and the Heisenberg exchange Hamiltonian for the ferromagnetic excitations (or spin waves). The translational symmetry along the length of the ribbon or stripe is utilized to make a wave-vector Fourier transform in this longitudinal direction, while the finite number of rows in the transverse direction are treated within a matrix formulation.