First Principle And Tight Binding Model Study On Several New Types Of Topological Materials

Since the discovery of the quantum Hall effect,topological theories have been continuously improved,especially in the past decade,topological theories and experiments have made breakthrough progress.As a new quantum state,topological materials have attracted extensive attention and became a research hotspot in the condensed matter physics and materials science.A large number of topological materials are theoretically predicted,and some of them have been experimentally confirmed.With the deepening of research,the types of topological states are constantly enriched,such as topological insulators,Dirac semimetals,Wely semimetals,nodal-line semimetals,triple-point semimetals,topological crystalline insulators,high-order topological insulators.The topological states always accompany by topologically protected surface states or boundary states with non-dissipative or very low-dissipative electron transport characteristics.The transport feature shows greatly potential in quantum computers,spintronics,and high-temperature superconductivity.From the view point of the advance of the topolotical materials,theoretical prediction plays a vital role for the realization and observation of the topotical materials in experiments.Therefore,predicting new topological materials and exploring new topological states can not only enrich the types of topological materials,but also provide the possibility of exploring the novel physical properties.Based on first-principles method,we predict that the anti-fluorite structure Be₂Si is a hybrid nodal-line topological semimetal.Based on symmetry analysis,we use k·p perturbation method and tight binding method to construct effective Hamiltonian models to thoroughly anslyze the topological origin of several topological materials.The main contents and conclusions of this paper are listed as belows:（1）Based on first-principles method in company with group theory symmetry analysis,we predict that anti-fluorite structure Be₂Si is a non-trivial hybrid nodal-line semimetal.The hybrid node line around the Fermi level is formed by Type-I and Type-II nodes,and is protected by time inversion symmetry,space inversion symmetry,and mirror symmetry,which provides an excellent platform to study the interaction and different characters between these two Dirac fermions.In addition,a new k·p model is proposed to analyze the topological origin of the hybrid nodal-lines.The existence of"eardrum"topological surface state in Be₂Si verifies its topological properties.The tiny gap induced by SOC indicates that Be₂Si is a promising candidate for future experimental studies of nontrivial topological semimetals;（2）We use the effective Hamiltonian model to analyze the topological origin of several topological states,including nodal-line topological semimetal,triple fermion semimetal,Dirac half-metal,and high-order topological insulator.We find that the double nodal-lines in Na Al Si are protected by mirror and time inversion symmetry;The triple fermion in YPt P are derived from the C_3Z and M₁₁₀ symmetry which lead to double degenerate and nondegenerate band inГ-A high symmetric line,and the double degenerate and nondegenerate band cross formed the triple fermion;The Dirac cone in the Dirac half-metal Mn₂Se₄ is derived from the off-center mirror symmetry.Finally,based on the tight-binding model,we predict that high-order topological insulating phases with zero-energy corner states can observed in the breathing kagome lattice,and the corner states is protected by C₃ symmetry and mirror symmetry.Through a simple analysis,it can be considered that the high-order topological phase is an extension of the Su-Schrieffer-Heeger model to two dimensions.The above emperical models will provide theoretical guidance for the realization of topological states in certain artificial systems.