Quantum Anomalous Hall Effect In Twisted-bilayer Graphene Quasicrystal

Quantum anomalous Hall effect,as a special class of topological physical property,has caused extensive research upsurge in recent years.However,due to its high requirements on the properties of materials,there are few experimental materials that can achieve high-temperature quantum anomalous Hall effect.In this article,we deviate from the limitations of traditional crystalline materials and turn our attention to the twist bilayer graphene system which has made significant progress in experiments recently.We used the twist bilayer graphene quasicrystal model at the rotation angle of 30° as a platform to explore its topological structure properties,realize the quantum anomalous Hall effect,and calculate the quantum anomalous Hall effect conductance by the Green's function method.The main structure of this article is as follows:The first chapter starts from the mechanism behind the quantum anomalous Hall effect,discusses the current status of theoretical research and the difficulties encountered when researchers try to achieve it.Then the construction method of alignment crystal model and some related work are explained.Moreover,the possibility of realizing quantum anomalous Hall effect on quasicrystal is given.Finally,the current research hotspots of graphene system are briefly introduced.We started from the superconducting phase and the magnetic mechanism found in the insulating phase from the electronic structure of the magic-angle twist bilayer graphene.Besides,we discussed the Dirac cone replica appeared in the twist bilayer graphene quasicrystal under the angle-resolved spectroscopy,which led to the main content of this article:whether the replica of Dirac cone in the twist bilayer graphene quasicrystal has special topological properties.The second chapter introduces the calculation method used in this paper,which provides a theoretical basis for the calculation of the topological number and electron transport of twist bilayer graphene quasicrystal in real space.The third chapter first introduces the construction method of the theoretical model of twist bilayer graphene,and discusses the related work on the processing method of twist bilayer graphene model.Secondly,the calculation of the energy band structure of the twist bilayer graphene quasicrystal is introduced,and the possible source mechanism of the Dirac cone replica copies is discussed.Thirdly,the topological properties of this model are studied,and the impact of the change of model parameters is discussed.Fourthly,we constructed the two-terminal transport system with the twist bilayer graphene quasicrystal as the scattering region,and then calculated its electron transport properties using the Green function,and compared it with the topological phase research results.Finally,the anti-disorder capability of the quantum anomalous Hall effect realized on the system is explored.The last chapter is a summary of the whole work and a discussion of the problems and future research directions in the work.