Theoretical Prediction And Study Of Two-dimensional Topological Materials

Exploring and researching novel topological states in electronic materials is one of the current hot topics in condensed matter physics.The main characteristic of topological materials is the presence of non-trivial surface or edge states,exhibiting exotic physical properties.With the massive research and rapid development of 2D materials,more and more candidate materials with rich and excellent properties have been successfully prepared experimentally,which gradually become a new fertile ground for exploring novel topological phases.In this paper,based on first principles calculations,we predict several different 2D topological materials and studied their topological properties.In chapter 1,we mainly introduce the developments of topological states in condensed matter physics starting from the Integer Quantum Hall effect,and provides a detailed account of the characteristics and research progress of several different topological materials,including first and higher order topological insulators(HOTIs)and various topological semimetals.In chapter 2,we introduce the main theories in our studies,including density functional theory(DFT)and Maximally Localized Wannier Function method.In chapter 3,we introduce a transition metal vanadium boride VB28 that is predicted to be a ferromagnetic Weyl semimetal by theoretical calculations.VB28 consists of two single layer boron sheets and vanadium atoms,with the vanadium atom located at the center of the hexagonal hole of the boron sheet.The structure exhibits both dynamic and thermodynamic stability.First principles calculations show that the ground state of VB28 is ferromagnetic,with the Curie temperature of about 34 K.The spin up bands show as a semiconductor,while the spin down bands exhibit as a half-metal,showing fully spin-polarized characteristics.The Berry phase and edge states calculated from the semi-infinite boundary structure confirm that the structure is a Weyl semimetal,protected by mirror symmetry and C2zT Combined symmetry.The Weyl points can be maintained under spin orbit coupling and are robust against various strains.This work enriches the family of magnetic Weyl semimetal materials and provides candidate materials for experimental studies of magnetic Weyl semimetals.In chapter 4,we introduce the existence of HOTI properties in two theoretically predicted porous graphene structures,C48 containing 48 carbon atoms and 6 vacancies,and C42O6 with 6 carbon atoms replaced around the hexagonal holes.The porous graphene C48 shows a zigzag boundary around the hole and it has dynamic stability.The total magnetic moment of the primitive cell is 6 μB,exhibiting ferromagnetism.Both spin up and spin down bands exhibit semiconductor behavior,with several flat bands above the Fermi level in the spin down channel.A tight-binding Hamiltonian is constructed using Wannier functions.The calculations reveal the existence of edge states in gaps of both spin,and the edge states in spin up channel is also gapped.A nanodisk is constructed and calculated.The results show the existence of corner states near the Fermi level,and the quantized quadrupole moment proves that it is a 2D HOTI.C42O6 is obtained as a nonmagnetic structure by replacing 6 carbon atoms,with a semiconductor band structure.The quantized quadrupole moment and the corner states localized at the corner of the nanodisk prove that it is a HOTI.This work predicts the existence of HOTI properties in two porous graphene structures and provides potential candidate materials for observing 2D HOTIs in experiments.In chapter 5,we introduce a 2D bilayer borophene predicted to be a HOTI.The structure of the bilayer borophene is formed by stacking two single layer boron sheets,which have internal buckling and interlayer bonding,and are dynamically stable.The electronic band structure shows a gap of 0.62 eV near the Fermi level,which becomes progressively smaller and eventually closes when the layer spacing decreases.A tightbinding Hamiltonian is constructed using the Wannier function method,onsite potential,intralayer hopping,and interlayer hopping are studied and controlled to find out the factors that affecting the band gap.Calculations on semi-infinite structures reveal that the edge states are gapped.Different nanodisks are calculated using both DFT and tight-binding model,and it is found that there are corner states near the Fermi level,which are robust against structural defects and perturbations.Our work predicts a stable 2D HOTI,which provides a candidate material for observing HOTI in experiments.