First-principles Study About The Electronic Structures Of Topological Compounds

Topological insulator?TI?is a new kind of material possessing gapped bulk states and exotic metallic surface states.The robust surface state in a 3D system,sheltered against backscattering from nonmagnetic impurities as long as the bulk gap remains open and the time-reversal symmetry is preserved.The unique feature of the surface state has attracted enormous attention in theoretical calculations and experimental observations,not only because of their theoretical importance but also because of their great potential applications.Recently,the topological properties have been extended into a variety of three dimensional?3D?topological semimetal?TSM?systems.In most Weyl/Dirac semimetals,conduction bands overlap with valence bands at certain momentum points.For instance,the topological properties of Na₃Bi and Cd₃As₂,semimetals have been experimentally confirmed.However,in line-node semimetals,the band crossing points around the Fermi level?E_F?form a closed loop.Many systems have been proposed as line-node semimetals including Mackay–Terrones crystal?MTC?,Bernal stacked graphene bilayer,antiperovskite Cu₃PdN and so on.Such line-node band structure has been measured by the angle-resolved photoelectron spectroscopy?ARPES?in PbTaSe₂ and ZrSi S.Interestingly,in addition to these materials,researchers also found node line structures in the photonics crystals and spin liquids.Their intriguing properties characterizing topological nodal line semimetals include drumhead like nearly flat surface states,unique Landau energy levels,long-range Coulomb interactions,which open an important route to achieve high-temperature superconductivity.The topological line-node semimetal could be driven into3D TI or Dirac semimetal by the SOC and strain.For example,CaTe is a TSM,possessing the nodal rings without SOC,exhibiting Dirac semimetal behavior when SOC is included.When it was applied by appropriate strain,it becomes a strong topological insulator.Those novel properties have attracted great research interest in recent years.In this thesis,based on the first-principles calculations and effective model analysis,we focus on line-node and Dirac semimetal and study the exotic quantum phenomena about them.The thesis including the following results:?1?.Based on fully relativistic first-principles calculations,we studied the topological properties of layered XIn₂P₂?X=Ca,Sr?.Band inversion can be induced by strain without SOC,forming one nodal ring in the k_z=0 plane,which is protected by the coexistence of time reversal and glid mirror symmetries.Including SOC,a substantial band gap is opened along the nodal line and the line-node semimetal would evolve into a topological insulator.Our investigations provide a new perspective about the formation of topological line-node semimetal under strain.?2?.By first principles calculations,we found that BaGaSnH is a topological Dirac semimetal with a pair of Dirac points at?0,0,±0.45?when spin-orbit coupling?SOC?is considered.The Dirac points are exactly at the Fermi energy,which makes the experimental measurement easy.The Dirac semimetal state and the topological properties are sensitive to the strain,which makes the compound enter the trivial semiconductor state.?3?.By first-principles calculations,we find that PbO₂ is a strongly topological node-line semimetal?NLSM?,which is protected by the coexistence of the time-reversal and spatial inversion symmetry when the spin-orbit coupling?SOC?is ignored.In the three dimensions Brillouin zone,there are two node-line rings around the?point,perpendicular to each other.It is different to the previously NLSM which has one or three node-line rings in the Brillouin zone.The drumhead-like surface states also can be obtained on both the 100 and 010 surfaces.When the SOC is included,a small gap opened along the nodal line,this material becomes a topological insulator.Therefore,our discovery renders an ideal platform for experimental exploration of the fundamental physics of topological node-line semimetals.