First-principles Study Of Transition Metal Topological Properties

Topological classification of material states provides a new perspective for us to understand the properties of matter.The discovery and understanding of topological materials is one of the hot topics in condensed matter physics in the last 10 years.Topological materials can be divided into topological semimetals,topological superconductors,topological insulators and so on according to their different non-trivial electronic structures.These materials exhibit many novel physical properties that cannot be described by classical physics,such as symmetry-protected topological surface states,symmetry-protected chiral symmetries,dissipation free transport and so on.These novel topological properties are expected to be in information technology,semiconductor technology and future industry.First-principles calculation,based on the basic principles of quantum mechanics,plays a key role in the study and analysis of the electronic structure of topological materials.With the development of this field,a large number of topological electronic materials have been predicted by theoretical calculations and then confirmed by experiments.In this paper,the electronic structures of a series of transition metal nitrogen compounds are studied and calculated based on First-principles calculation method,and the related properties are analyzed and compared with experimental data.The main structure of this paper is as follows:First of all,we mainly introduce the research background and the development of topological states,including the theoretical knowledge of Berry phase,the concept and development of topological insulators,Dirac semimetals,Weyl semimetals and nodalline semimetals.secondly,we mainly introduce density functional theory,pseudopotential method and Wannier function method theory.This part is the theoretical basis of our subsequent theoretical calculation work.We mainly introduce the valence electron approximation and Born-Oppenheimer approximation,Hohenberg-Kohn principles,single electron approximation,Hartee-Fock appro-ximation,pseudopotential derivation and selection,Wannier function and maximally localized Wannier function.We calculate the electronic structure of Dirac semimetall SrAgAs using first principles method.The energy band calculation results show the clean electronic structure near the Fermi-surface of the material,and the crossing of the energy band after considering the spin-orbit Coupling(SOC).The energy band structure and Fermi surface are studied in detail and compared with the results of dHvA.Meanwhile,the electronic structure calculation results of low dimensional magnetic layered material Fe3-xGeTe2 are introduced,and the Hall conductivity and Nernst signal changes with temperature and doping are mainly studied.The results explain the sign change of Nernst signal and the variation of Hall conductivity due to the competition between Weyl points near Fermi energy at different iron vacancy levels.Last,the similarities and differences of electronic structures of XB6(X=Y,Sr,La)series compounds are introduced,including crystal structure analysis,energy band structure,Fermi surface,phonon spectrum,electron phonon coupling constant ?,superconducting transition temperature Tc.The results show that the electron phonon coupling strength of Yb6 is much higher than that of LaB6 and SrB6 for the three compounds with the same crystal structure,and the compound shows superconducting properties.The special electronic structure of SrB6 shows that it has the properties of topological semimetals.Our calculations suggest a possible route to obtain materials with coexisting nontrivial topology and superconductivity by mixing SrB6 and YB6.