First-principles Study Of The Three-dimensional Topological Electronic Materials

Topology originated from the theory of seven Bridges in Europe and was later developed by the mathematical world as a science of space and dimension.In recent years,topology theory has expanded to the field of condensed states,called as topological insulator(TI).It has a non-trivial topological band structure and exhibits unique physical properties,such as: its body state has an energy gap similar to ordinary insulators,but the surface shows a metal-like surface state,When the surface state is protected by time inversion symmetry,impurities and disorder cannot destroy it.With the continuous development of topology,topological materials have expanded from TIs to the topological semi-metal(TSM)field,such as: Nodal Line semi-metal,Dirac semi-metal and Weyl semi-metal.Compared with TIs,near the Fermi energy level,non-mediocre band crossings occur in TSM,and the dimensions of the band crossings have zero-dimensional(nodal point,such as Dirac / Weyl semi-metal)and one-dimensional(nodal loop)and two-dimensional(nodal surface).Topological electronic materials have become a very popular research direction in condensed matter physics due to their new band structure and strange physical properties.In this paper,in the process of mining and researching topological electronic materials,the first-principles calculation method has played an irreplaceable role and has been implemented consistently,for example: from the initial search for materials to the further determination of stable ground states,the analysis of band structures,predictive magnetism,etc.Using the first-principles calculation method based on density functional theory and k · p model analysis,we mainly do detailed research on the following topological electronic materials.The specific research process is as follows:1,We studied the band structure and topological properties of the intermetallic compounds Sc-TM(TM =Cd,Ag,Cu,Hg,Au),by using the first-principle calculations.The Sc-TM is experiment has been synthesized in the non-magnetic material,they crystallize in the simple cubic structure(space group Pm(?)m,No.221),with space inversion symmetry.After simulation and energy band analysis,we find that these intermetallic compounds are topologically nontrivial Multi-Nodal-Lines semimetals in the absence of the spin-orbit coupling(SOC).Unlike the previously reported nodal-line semimetals with nodal-lines inside their Brillouin-zones(BZ),the nodal-lines of the Sc-TM intermetallic compounds lie on six BZ surfaces,protected by the space inversion and time-reversal symmetries.The nodal-line induced drumhead liked surface states are obtained on the(001)-surface.When the SOC is included,a small band gap opens along the nodal lines.This indicates that these intermetallic compounds become topological insulators(TIs),on contrary to the general expectation that IMCs will be metals.2,Using the first-principle calculations and k·p model analysis,we predicted a new topological semimetal(TSM)MgBi₂O₆.The MgBi₂O₆ crystallizes in the tetragonal crystal structure with space group P42/m n m(No.136)at ground state.Without SOC and under the generalized gradient approximation(GGA),MgBi₂O₆ is a nodal-line semimetal.When the exchange-correlation energy was changed to HSE06,MgBi₂O₆ was trivial insulator in the equilibrium volume,but it became TSM under 7% hydrostatic tensile strain.MgBi₂O₆ might be an important platform to study the topological properties because of the two following advantages for measurements:(1)The nodal line,drumhead-liked surface state and Fermi Arc are very closely to the Fermi level;(2)The band structure is very “clean”(no other bulk bands except the related inverted conduction and valence bands around the Fermi level),which avoids the surface states been embedded into the bulk states.