Theoretical Investigation On The Electronic Properties Of Topological Weyl Semimetals In F(?)3m Space Group

The field of topological materials has developed rapidly,since the discovery of quantum Hall effect.In the last ten years,many new types of topological materials have been proposed.Nowadays,the concept of topological materials are introduced not only in electronic systems but also in photonics systems,phonons systems,magnetons systems and other systems.Topological electronic materials are the focus of our study.The surface states of the topological electronic material makes the electrons that were transmitted relatively mess more regular.In particular,the Fermi arcs of Weyl semimetals,as a highly efficient conductive channel,are expected to reduce the heat dissipation of electronic devices.And the resistance of topological materials to external perturbations also makes them more useful.In the study of topological materials,we used a first-principles calculation method to do numerical simulations.Numerical simulation is one of the bonds between theory and experiment in the field of condensed matter.The three pillars complement each other,making the study of electronic properties clearer.We predicted a possible non-magnetic Weyl semimetal CrAlTiV which has F(?)3m space group based on first-principles.And other researchers have found some other compound with similar properties in the same space group.We discussed them separately with the k · p model and band representation.In Chapter 1 and the Chapter2,first of all,we briefly introduce the development of topological materials,and the basic knowledge of topological band theory is included.Secondly,we introduce some theoretical knowledge and calculation methods.For the density functional theory which the first principle relies on,we introduce the Hartree-Fock theory,the Thomas-Fermi theory,the Hohenberg-Kohn theorem,the Kohn-Sham equation and the exchange-associative functional.We also introduce the Wannier function which is used to construct the tight-binding model.The tight-binding model is used to project the surface states.We also introduce Berry phase which is the important concept of the topological band theory.Finally,we briefly introduce the calculation software tools.In Chapter 3,We predict that the paramagnetic state of inversion-breaking quaternary Heusler alloy CrVTiAl is a Weyl semimetal candidate.There are 24 Weyl nodes(WN)appearing at the same energy in the first Brillouin zone without spin-orbit coupling(SOC).One WN splits into a pair of Weyl nodes(WN1 and WN2)of the same chirality when considering SOC because SOC removes the spin degeneracy.Clear surface state Fermi arc structures on the(111)surface are also obtained.The formation mechanism of the Weyl nodes is independent of point symmetries,i.e.,the number and chirality of Weyl nodes are not affected when the point symmetries are broken slightly.In Chapter 4,we introduce the non-magnetic Weyl semimetal InSTl which have the same space group with CrVTiAl.The Weyl nodes has the same properties as the Weyl point of CrVTiAl.The Weyl points locate at the edge of the Brillouin zonek when the spin-orbit coupling is not considered.And they split into a pair of Weyl nodes,when spin-orbit coupling is considered.Subsequently,we used the k · p model to analyze the effective Hamiltonian of InSTl and CrAlTiV.In Chapter 5,we analyze the energy band representation in the space group F(?)3m without considering the spin-orbit coupling and considering the spin-orbit coupling separately.Regardless of the spin-orbit coupling,for the p-orbit of InSTl,a double degeneracy point is generated on the high symmetry line V which is the predicted Weyl point.In the case of considering spinorbit coupling,the inversion of the energy band occurs on the high symmetry line V.It proves that there are topologically nontrivial electronic states in these bands.The Chapter 6,we summarize the work of this paper and prospect the future work.