Moreau, Nicolas
[UCL]
Charlier, Jean-Christophe
[NAPS]
When submitted both to a magnetic field and a periodic potential, the energy spectrum of electrons exhibits a fractal-like pattern known as Hofstadter’s butterfly. Proofs of the existence of this butterfly were reported in a moiré lattice of graphene on hexagonal-boron-nitride (hBN) in 2013. In this master thesis, two main tight-binding (TB) models are developed to study the butterfly in similar moiré systems. The first model considers the effect of hBN as a periodic electrostatic potential that modifies the on-site terms of graphene TB Hamiltonian. The second model is based on a complete TB approach. Interactions between graphene and hBN are performed by interlayer bond energies. The values of those interlayer parameters have not yet been reported in literature. In this thesis, they are determined with DFT calculations. Based on those two models, the electronic properties of graphene on hBN are discussed first. Character- istic features, such as the gap opening at the Dirac point, the appearance of secondary Dirac points, and the geometrical influence of the moiré pattern are properly described by the complete TB model. In the latter part of the thesis, the signature of the butterfly is highlighted and compared with corresponding experimental results.
Référence bibliographique |
Moreau, Nicolas. Development of a tight-binding model to study Hofstadter’s butterfly in graphene on h-BN exhibiting a moiré pattern. Ecole polytechnique de Louvain, Université catholique de Louvain, 2017. Prom. : Charlier, Jean-Christophe. |
Permalien |
http://hdl.handle.net/2078.1/thesis:10714 |