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

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.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Lancaster University

Year dc:date.issued

2015

Authors dc:creator

• Chen, Xi
• McCann, Edward