Topologically-Protected Soliton States in Rhombohedrally-Stacked Graphite

Muten, James and McCann, Edward (2024) Topologically-Protected Soliton States in Rhombohedrally-Stacked Graphite. PhD thesis, Lancaster University.

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Abstract

We investigate the low-energy electronic properties of rhombohedrally-stacked graphite (RG). Chapter 1 discusses the history of graphene and provides the context for our work. In Chapter 2 we introduce the tight-binding model and demonstrate its application in describing the Hamiltonians and electronic band structures of several graphitic systems. We also present three one-dimensional models describing topological insulators, and show, through dimensional reduction, that these are similar to the graphene systems under investigation. Chapters 3 and 4 describe the original research work in the thesis. Chapter 3 describes stacking faults in thin films of RG.We find that each stacking fault produces two localised low-energy states near the Dirac points. In comparison to the one-dimensional models, such faults are effectively a soliton-antisoliton pair, and it is impossible to realise a single, isolated state on a stacking fault in RG. In Chapter 4 we consider rhombohedrally-stacked systems with alternating onsite energies, and, particularly, the properties of solitonsconsisting of a change in texture of the onsite energies. We show that, depending on parameter values, a single localised energy band may be isolated within the bulk band gap, in contrast to stacking faults in RG. For both types of faults, in Chapters 3 and 4, we derive low-energy effective Hamiltonians to describe hybridisation of the localised soliton states with localised surface states, and we model the robustness of the properties of these states in the presence of disorder.