First-principles Study On The Quantum Anomalous Hall Effect Of Two-dimensional Graphene-like Materials

The quantum anomalous Hall effect is a mode of unimpeded transport of electrons.It has a chiral boundary state at the sample boundary.But the quantum anomalous Hall effect took more than 20 years from predicting to discovering.Because the realization of the quantum anomalous Hall effect requires a very special material system and method.Under scientists'communications,topological insulators have come into everyone's vision.Topological insulator is a new quantum state of matter which is different from traditional metals and insulators.Topological states are a kind of novel quantum matter states which areinsulating in the bulk but exhibit unique gapless edge states protected from elastic backscattering due to the nontrivial topology of the bulk electronic states.This non-dissipative ballistic transport feature has potential application value in future quantum computers and spin electronics.If this discovery can be applied,supercomputers may become i Pad-sized handheld notebooks,and smartphone memory may exceed thousands of times of the most advanced products.In addition to long standby time,it will also have a speed that inconceivable to contemporary people.In this thesis,we have studied the quantum anomalous Hall effect in two low-dimensional material systems.The first chapter introduces the research background of topological insulators,and then introduces the basic concepts and research progress of integer quantum Hall effect,quantum spin Hall effect,and quantum anomalous Hall effect,as well as the concept of topological invariants.The second chapter introduces the theoretical basis of first-principles calculations,including the concepts and principles of density functional theory,and also introduces some exchange correlation functions and calculation software packages commonly used in the calculation process.In Chapter 3,we studied the heterogeneous structure of three types of graphene/Cr Br₃(Gr/Cr Br₃)using first-principles calculations.However,pressure-induced Anomalous quantum Hall effect can be achieved in Gr/Cr Br₃and Cr Br₃/Gr/Cr Br₃systems.Further analysis of the low-energy k·p model shows that the non-mediocre topological properties are mainly due to Rashba spin-orbit coupling(SOC),not the intrinsic SOC of graphene.This provides a broad opportunity to implement graphene-based quantum anomalous Hall effect(QAHE).In Chapter 4,we propose that the band inversion between p_x,y,and p_zorbitals can produce a topological phase transition in a honeycomb hexagonal lattice based on a tight-binding model analysis.In the two sub-lattices(AB sub-lattices)of the graphene-like hexagonal lattice,the p_x,y,and p_zorbitals are introduced respectively,and the topological phase transition can be achieved by adjusting the strength of the spin orbit coupling(SOC).Based on the first-principles,two systems of half-iodinated silicene(Si₂I)and one-third monolayer of bismuth epitaxially grown on the Si(111)-3×3are used to achieve the topological state caused by p_x,,y,and p_zband inversion.This proves the correctness and universality of the mechanism.The fifth chapter summarizes the previous work and looks forward to the future work direction.