# Electronic Phenomena In Graphene Based Van Der Waals Heterostructures

• Joshua Thompson

Student thesis: Doctoral ThesisPhD

### Abstract

In this thesis, we model the electronic and optical properties of stacked structuresof two-dimensional materials involving graphene. In particular, we discuss howthe interplay between the type and alignment of these stacked two-dimensionalcrystals affects the observed physical properties.Tuning the misalignment between two graphene layers leads to stark modi-cation to the resulting electronic band structure. By employing electronic Ramanscattering, we show that it is theoretically possible to accurately determine thetwist angle in twisted bilayer graphene samples close to the magic-angle.We propose a new parameterisation for the interlayer coupling between twistedgraphene layers, and demonstrate that twisted trilayer graphene is the simplestsystem in which the coupling in aligned and misaligned graphene bilayer can beprobed. By comparison to experimental photoemission data, we demonstrate thevalidity and self-consistency of our model.We discuss the tunnelling current across two van der Waals tunnelling transistors.In the rst, one or both of the electrodes are made of two crystals forminga moir\'{e} superlattice at their interface. We investigate structures containing eitheraligned graphene/hexagonal boron nitride heterostructure, twisted bilayergraphene or aligned graphene on $\alpha$- In2Te2 and show negative dierential resistanceis possible in such transistors. In the second case we propose a tunnellingjunction in an external magnetic eld perpendicular to the layers, wherethe source and drain electrode are comprised of bilayer and monolayer graphenerespectively. We show that, due to the effective difference in tunnelling barrierwidth for electrons on the two layers of bilayer graphene and the valley-dependentwave function distribution between these layers, the valley polarisation of the currentcan be electrically tuned. We demonstrate that strong valley polarisationcan be obtained in the clean limit, where strong-momentum conserving tunnellingdominates, and in lower quality devices where this constraint is lifted.
Date of Award 2 Oct 2019 English University of Bath Marcin Mucha-Kruczynski (Supervisor) & Kei Takashina (Supervisor)

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