The Study On Quantum Transport Properties In Graphene-Based Van Der Waals Heterostructures

In the last decade,topological electronics becomes a hot topic in condensed mat-ter physics,such as topological insulators,quantum anomalous Hall effects,and Weyl semi-metals.The general consensus is that the theory of Berry curvature can success-fully explain the origin of topological properties.The basic concept of the theory is that in the presence of an electric field electrons can obtain an anomalous velocity,which is proportional to Berry curvature and perpendicular to the direction of the electric field.The velocity can essentially affect many transport phenomenon,such as various types of Hall effects.The topological band structure has insulating bulk states and conducting edge states.The edge states in the system will be destroyed by inducing strong non-magnetic disorder and thereby the system will transit into Anderson insulator.Thus a fundamental problem arises:how the edge states destroyed in the presence of magnetic disorder?Another type of transport phenomenon induced by disorder is universal conduc-tance fluctuation.It is a mesoscopic quantum interference effect which occurred in the case of that the sample size is less than the phase coherence length,and the fluctuation amplitude only depends on the dimensionality and symmetry of the system.Although a lot of researches concerned about universal conductance fluctuation in integer dimen-sions,it is unknown that whether exists universal conductance fluctuation in fractal dimension.Recently the fractal lattice has been realized experimentally by molecular self-assembly.Therefore,it is important to study universal conductance fluctuation in fractal dimension.Besides the novel transport phenomenon induced by disorder,recently with the discovery of two-dimensional materials such as graphene,hexagonal boron nitride and transition metal dichalcogenides,the related transport studies have also received much attention.Since mainly formed by weak van der Waals interaction,different types of layered materials can be stacked to build the van der Waals heterostructures,which can provide additional controllable degrees of freedom such as the number of layers,the twist angles,and so on.The band structure and transport properties can be modified by these special degrees of freedom.Established researches usually consider the intralayer transport properties.But the mechanism of interlayer transport is still unclear.There-fore,it is necessary to explore the vertical transport properites between layers in van der Waals heterostructures.Based on above purpose,we have carried out the corresponding theoretical re-search on electron transport.The content of this thesis includes the following five chap-ters:In Chapter 1,we introduce the history of various types of Hall effects,the influence of Berry curvature on electron motion in an electric field,the basic concept of van der Waals heterostructures,and recent progress of the application of electron transport in van der Waals system.In Chapter 2,we utilize tight-binding method to study Anderson localization in-duced by magnetic disorder in quantum anomalous Hall effect system.By calculating the evolution of conductance and the Berry curvature at different Fermi velocities,we find a new mechanism of Anderson localization that as the disorder strength increases,the interchange of Berry curvature in conduction and valence bands will lead to the sys-tem undergo a phase transition from quantum anomalous Hall insulator to metal and finally to Anderson insulator.In Chapter 3,we use tight-binding method to study the conductance fluctuation of the Sierpinski lattice in different ensembles.We find that there exists universal conduc-tance fluctuation in both circular unitary ensemble and circular symplectic ensemble with a value of 0.74±0.01 e2//h.After analysis of the conductance distribution we find that the two ensembles follow the same distribution functions.In Chapter 4,the vertical transport properties of graphene-based heterostructures are studied by using the tight-binding method.We find that with the change of the length of central scattering region,there exists quasi-periodic oscillations and saturation of conductance in the systems of different types of boundary.Then we analyze the origin of the two phenomenons.In Chapter 5,we use first-principles transport method based on the non-equilibrium Green's function to study the vertical transport properties in a mesoscopic twisted bi-layer graphene device.We investigate the dependence of interlayer conductance on the rotational axis,system size,rotation angle and Fermi energy.We find some novel electronic transport properties in such system.Chapter 6 is the summary and outlook of this thesis.