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  • 2015Chenphd

    Accepted author manuscript, 24.2 MB, PDF document

    Available under license: CC BY: Creative Commons Attribution 4.0 International License

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The Hofstadter spectrum of monolayer and bilayer graphene van der Waals heterostructures with boron nitride

Research output: ThesisDoctoral Thesis

Published
Publication date2015
Number of pages213
QualificationPhD
Awarding Institution
Supervisors/Advisors
Publisher
  • Lancaster University
<mark>Original language</mark>English

Abstract

In this thesis, we consider the electronic properties of materials created by stacking two-dimensional graphene layers. The first material is a heterostructure created by placing a graphene layer on top of a layer of hexagonal boron nitride. The energy bands are determined as well as the energy spectrum in the presence of a magnetic field applied in the direction perpendicular to the layers. There is a miniband structure that includes gaps and secondary Dirac points as well as a fractal structure of magnetic minibands known as Hofstadter's butterfly. The second material is multilayer graphene, which consists of a small number of graphene layers stacked on top of one another. We determine the effect on the low-energy electronic band structure by applying a magnetic field in the direction parallel to the layers, and find that the parallel field can induce a dramatic change in the band structure, which is known as a Lifshitz transition. Furthermore, depending on the magnitude and the direction of the field within the plane of the graphene layers, it is possible to access different phase regions of the band structure. We also model the electronic transport properties of multilayer graphene. We use both analytical mode-matching and the numerical recursive Green function methods to study the transport properties of electrons in multilayer graphene in the vicinity of zero energy, zero temperature and zero magnetic field.