First-principles Study Of Ternary 4d Transition Metal Superconducting Compounds

Superconducting materials have rich physical properties and are one of the main research field of condensed matter.In this thesis,the electronic structural properties of transition metal compounds K₂Mo₃As₃and Cu Rh₂Se₄are mainly studied based on the first-principles calculation of density functional theory,and study their topological properties by substitution doping of transition metal elements in Cu Rh₂Se₄.In the first part of this thesis,the development background of superconductivity and energy band topological properties is introduced,including iron-based and copper-based unconventional superconductivity,topological insulators,topological semi-metals,etc.In the following chapter,we introduce density functional theory,topological insulators and Z₂topological invariants,which are also the main theoretical basis of the subsequent parts of this thesis.Among them,we focus on Hartree-Fock approximation,Hohenberg-Kohn theorem,Kohn-Sham equation,exchange correlation functional and calculation of Z₂topological invariants.We then apply these methods to study the electronic structure and band topology of K₂Mo₃As₃and Cu Rh₂Se₄.We calculated the electronic structure of K₂Mo₃As₃using first-principles method.Without considering spin-orbit coupling（SOC）effect,there are three bands passing through Fermi energy level,of which two bands only pass through Fermi energy level along k_zdirection,resulting in two parallel one-dimensional Fermi surface.Along theΓ-Ζpath,we can see that there are two degenerate energy bands passing through Fermi level,and these two pairs of sheet Fermi surface also show one-dimensional properties in electronic structure.When SOC is considered,the bands near the Fermi level will split,and the three bands passing through Fermi level split into six bands.At the same time,we also analyzed the Fermi surface of this compound.Without considering SOC,K₂Mo₃As₃Fermi surface consists of a three-dimensional Fermi surface with peanut-like structure and two quasi-one-dimensional Fermi surface.After considering SOC,the Fermi surface will split into two parts,and at the same time,two adjacent quasi-one-dimensional Fermi surface sheet will be formed.Finally,we calculated the bare electron susceptibility of K₂Mo₃As₃,and the imaginary part of K₂Mo₃As₃has a significant peak near theΓpoint,it requires further verification and research to determine if it is related to ferromagnetic spin fluctuation.For CuRh₂Se₄ compound with spinel structure,we studied its normal electronic structure and topological properties.and analyzed the influence of transition metal elements doping（Os,Pd,Pt,Ru）.It is found that the electronic states near Fermi level are mainly contributed by Se-4p,Rh-4d and Cu-3d orbitals.Because the system has spatial inversion symmetry,the spin-orbit coupling does not lift the spin degeneracy.When considering the SOC,two doubly degenerate bands pass through Fermi level,resulting in three doubly degenerate Fermi surfaces,including a pair of drum-like Fermi surface,a pair of cross-like Fermi surface at the regional boundary and a pair of star-like Fermi surface aroundΓpoint.We have studied the electronic structure of 1:1doped compound at Rh position with Os,Pd,Pt and Ru,using virtual crystal approximation（VCA）approximation.We found that the hole-doped Cu（Rh,X）₂Se₄ is an energy band topological insulator.