PhD dissertation, defended on December 19, 2019.
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Condensed Matter Theory (CMT) group
University of Antwerp - Library
In the research field of two-dimensional materials, computational modelling proves to be crucial in examining the electronic properties. This increases the experimental throughput and broadens our understanding of the fundamental phenomena. Furthermore, it presents a theoretical foundation for developing a concept of materials by design, where the goal is to achieve a desired functionality. Still, the accuracy that atomistic modelling offers proves to increase the already demanding computational complexity. In this thesis graphene heterostructures and moiré patterns are tackled starting from a tight-binding (TB) atomistic description in real-space, with the use of numerical approaches proposed as an alternative to the traditional exact diagonalisation techniques. Spectral methods that scale linearly with the system size and their implementations in two open-source codes, Pybinding and KITE, offer the possibility to simulate complex large-scale systems, such as the ones investigated in this thesis.
Firstly, delaminations in graphene together with a theoretical concept of a graphene diode are discussed. Boundaries between different stacking arrangements in bilayer graphene are proven to host electrostatically induced topological states that can act as transport channels in a nearly dissipationless regime, due to the weak backscattering. Furthermore, boundary states are discussed and directly compared to the experimental measurements in the case of twisted bilayer graphene (tBLG). The effects on the electronic properties and the signatures in the transport are shown.
Secondly, recent experimental results on the tuning of the electronic properties by periodically strained graphene superlattices formed as a consequence of a buckling transition are modelled with a periodic pseudo-magnetic field (PMF). The spectrum reconstruction and the transition to the flat band regime is examined as a function of the superlattice period and the strength of the PMF. It is shown that the different flat bands possess different spatial localisation, where there exist flat bands that percolate throughout the sample. These results match the experimental investigations of our collaborators.
Lastly, the appearance of multiple moiré patterns in encapsulated graphene closely aligned to two hexagonal boron-nitride (hBN) layers is examined. At low rotation angles energy reconstruction is observed, an effect that can be explained as a second-order scattering event at periodicities which correspond to the interference between the individual moirés. Furthermore, it is shown that the resulting super-moiré (SM) interference has a strong effect on the structural properties. We show that the SM is imprinted both in the interlayer spacing and in the bond-length as a consequence of lattice relaxation and further enhances the spectrum reconstruction. The SM description helps in explaining a recent experimental study and provides another path towards achieving tunable superlattice bands in 2D materials.