Topological Properties Of Hybridized Dirac States In Transition Metal-based Two-dimensional Systems

It is recognized that two-dimensional materials only with atomic thickness do exist stably in nature after graphene has been achieved by mechanical exfoliation in2004.This discovery has stimulated extensive and in-depth research by researchers on a variety of two-dimensional materials.The most striking of these two-dimensional materials is the Dirac materials.Dirac materials mean that its low energy electron behavior can be described by the Dirac equation of relativistic quantum mechanics,and this electron energy-momentum dispersion relation is called the Dirac band.Graphene is the most representative two-dimensional Dirac material.Graphene has many excellent properties,such as high electron mobility,massless fermion and can achieve quantum spin Hall effect.These rich physical properties prompt people to look for more two-dimensional Dirac materials.Dirac materials are also considered as basis for next-generation microelectronic devices.This thesis is divided into five chapters.In chapter one,we first introduced the classification of two-dimensional materials,then introduced the Dirac equation and several representative two-dimensional Dirac materials,and last presented the current research status of two-dimensional transition-metal materials.In chapter two,we introduced the density functional theory（DFT）and the calculation methods required in this paper.In chapter three,we studied the electronic structure of 5d transition metal hafnium（Hf）adsorbed on the surface of graphyne（denoted as Hf-graphyne）.We have determined that the natural honeycomb large hole of graphyne is the ideal location site for adsorption of Hf atoms by the calculation of adsorption energy.Molecular dynamics simulations confirm the system’s thermodynamical stability approaching room temperature.The electronic structure of the whole system using hybrid functional calculation shows that the Hf-graphyne is ferromagnetic,and there are three Dirac points near the Fermi level.One of which is contributed by the d_z2 orbital of the Hf atoms,and the other two is the hybridization between d_xy/x2_-y2 orbitals of Hf atoms and p orbitals of the C atoms.We analyzed the reasons for the occurrence of these three Dirac points due to the interaction between the graphyne C atoms and the Hf atoms.Topology calculation shows that the gap of two Dirac states composed of hybridization orbits under considering spin-orbit coupling is nontrivial,and Chern number C=-3 is found.Therefore,quantum anomalous Hall（QAH）effect can be realized in the Hf-graphyne.In chapter four,we first optimized the free-standing two-dimensional honeycomb monolayer composed of Ta,W,Re,Os,Ir and Pt atoms by first principle software VASP and calculate their energy bands.We found that these two-dimensional transition-metal monolayers are metallic nature.Ta and W free-standing monolayer are non-magnetic and the other four are weak ferromagnetic.In their energy bands,Dirac states contributed by d_yz/xz and d_z2 orbitals are found,but these Dirac points are at deep energy levels and energy bands are interlaced and complex near Dirac cone.Subsequently,we considered the effect of strain on the electronic structure of these two-dimensional transition-metal materials.When the lattice constants of these transition-metal monolayer is increased by 50%,these materials have strong ferromagnetic.In the electron spin-down bands of Ta,W,Re,Os and Ir monolayer,the Kagome bands is formed,which composed of the Dirac band intersecting with a flat band above it intersects at high symmetricalΓpoint.However,the flat band is below the Dirac band in Pt monolayer.The orbital projection analysis and spin polarized orbital projected density of states（PDOS）show that the flat band is mainly contributed by the d_xy+d_x2_-y2 orbitals of the transition-metal atoms,while the energy band near the Dirac point is mainly derived from the s orbital.After the lattice constant of these free-standing structures stretch 50%,the charge density in these structures are centered on the transition-metal atoms to form a triangle of two shared vertices,so that the charge density constitutes the distribution similar to that of the Kagome lattice,giving rise to the appearance of the Kagome bands.Then we take the Os as an example to discuss the electronic structure of Os honeycomb crystal under different strain,the evolution of s+d_xy/x2_-y2 orbitals components,and the origin of the magnetism in the system.Finally,we consider the topological properties of the hybridization Dirac point composed of s+d_xy/x2_-y2 orbitals in two-dimensional Os honeycomb structure after strain equaling 100%.The calculated results show that the energy gap opened at the Dirac point is 22.5 meV after considering the spin-orbit coupling,and it is a nontrivial gap with Chern number C=-1.In chapter five,a summary of our work is given and we also prospect the future research aspects.