Theoretical Study Of The New Topological States In Graphene

Graphene, a new two-dimensional carbon material, has brought great interest in the scientific community due to its particular electronic properties. The research of the quantum topological properties in graphene under different environments is of great significance for the development of the next generation of nanoscale electronic devices. In this thesis, we mainly study the quantum Hall effect in graphene superlattice system and find a new quantum Hall state-valley chiral Hall state. The thesis is organized as follows:In the first chapter, we introduce some basic properties of graphene such as the lattice structure and the band structure. Meanwhile, we describe several commonly used theoretical approaches to calculate the electron transport properties of graphene. In addition, we also briefly introduce the traditional quantum Hall effect in order to compare with the anomalous quantum Hall effect in graphene.In the second chapter, we mainly introduce the tight-binding model and a numerical method to calculate the Hall conductivity. On this basis, we calculate the quantum Hall effect in monolayer and bilayer graphene. The results show that in the center of the energy band, the plateau at zero axy is markedly absent in these two systems. However, in bilayer graphene, the two lowest Landau levels lie exactly at zero energy and the Hall conductivity undergoes a double-sized step across this region. Meanwhile, we study the quantum valley Hall effect in monolayer graphene with a staggered sublattice potential by using low-energy continuous model and the Kubo formula. These results are consistent with the literature reported.In the third chapter, we investigate the new quantum Hall states related to the valley in graphene-In2Te2 superlattice by adopting the analytical derivation and numerical calculation methods. In the presence of an external magnetic field, graphene superlattice exhibits the ordinary quantum Hall effect with the Hall conductivity quantized as σxy=νe2/h(ν= 0, ±1, ±2,...) in the band center. At the zeroth Hall platform, a valley-chiral Hall state steming from a single K or K’valley is found. It localizes only in one boundary of the sample while the other boundary keeps insulating. So, it contributes to the longitudinal conductance but not to the Hall conductivity.In the fourth chapter, we make a summary of this thesis and put forward some expectations for future research.