Theoretical Studies Of Topological Semimetals

Topological semimetals are new topological states of matter and have become a hot topic in recent years due to their novel gapless electronic excitations and responses to electric and magnetic fields.Weyl semimetals,the typical topological semimetals,host discrete gapless points at the Fermi level,which can be described by the Weyl equation from high-energy physics.These gapless points,called Weyl points,can lead to many novel features,such as open surface Fermi arcs,negative magneto-resistance,chiral anomaly and chiral magnetic effects.In this thesis,we have two topics:One is developing new methods to construct effective models efficiently,and the other is to study the novel properties of topological semimetals by combining these new methods and first-principles calculations.Firstly,we introduce two ways to construct k · p models,i.e.k·p perturbation and method of invariants.We use these two methods to derive the Luttinger model,which will be used in the 3rd chapter.We also introduce a new method proposed by Gresch,which can directly get k·p models without manually picking suitable group representations.Based on his method,we make a modification and expand the range of applicability for the nonorthogonal matrix basis.Inspired by the method stated above,we also develop a method to construct the simplified tight binding models.Secondly,we show that HgTe and half Heusler compounds,under a broad range of in-plane compressive strain,could be materials in nature realizing ideal Weyl semimet-als with four pairs of Weyl nodes and topological surface Fermi arcs.We propose a simple model which shows that the HgTe-class materials with nontrivial band inver-sion and noncentrosymmetry provide a promising arena to realize ideal Weyl semimet-als.We also find four chalcopyrites(CuTlSe2,AgTlTe2,AuTlTe2和 ZnPbAs2)are ideal Weyl semimetals,without applying any external strain.The structure distortion in chal-copyrites leads to an effective compressive in-plane strain,which is the key for these compounds to realise ideal Weyl states.These ideal Weyl semimetals provide a unique platform to study the intrinsic properties of Weyl fermions and emergent phenomena.Thirdly,we investigate three-dimensional non-Hermitian nodal-line semimetals in the presence of a particle gain-and-loss perturbation.It is found that this perturbation will split the original nodal ring into two exceptional rings(ERs).The topological na-ture of the bulk electronic structure is characterized by two different topological invari-ants,namely,the vorticity and the winding number defined for a one-dimensional loop in momentum space.The conventional bulk-surface correspondence in non-Hermitian nodal-line semimetals is found to break down,where the surface zero-energy flat bands are no longer bounded by projections of bulk ERs.Alternatively,a macroscopic frac-tion of the bulk eigenstates can be localized near the surface,thus leading to the so-called non-Hermitian skin effect.Finally,based on the k·p perturbation theory,we propose that band inversion can induce saddle-like dispersion near the Fermi level.This theory can be applied to many two-dimensional and three-dimensional topological systems.We calculate three differ-ent materials as examples,including two-dimensional topological insulator WS2 and three-dimensional topological materials Na3Bi and Bi2Te3.The log-type divergency of density of states induced by saddle surface,can amplify electron correlation,resulting in different instabilities such as superconductivity and charge density wave.