First-Principles Study On Several Topological Semimetals

Topological materals have attracted great interest since topological insulators have been proposed in 2007.From then on,theoretical analyses,computational pre-dictions and experimental progress of topological materials all have obtained great achievements,the family of topological materials is becoming larger and larger:such as topological crystalline insulators,topological superconductors,node-line semimetals,nodal chain semimetals,hopf-link semimetals,nodal surface semimetals and so on.A-mong them,Weyl semimetals have showed many interesting properties,such as surface Fermi arcs,negative magneto-resistance,chiral anomaly and chiral magnetic effects,while node-line semimetals have exhibited drummed-like and even helicoid surface s-tates within some nonsymmorphic symmetries.In fact,nowadays,seeking for various topological phases with theoretical calculations and imposing symmetry-broken routine or extra fields to obtain topological phase transitions are very hot subjects.After a brief review and summary of the topological materials and the first-principles calculations,we first discuss pressure/strain induced quantum topological phase transition in the Dirac semimetal Na₃Bi system in the first part of this thesis.Both structure-searching results and the dispersion of phonon indicates that hydrostatic pressure can induce a structural phase transition of Na₃Bi from the space group of P???c1 to Fm???m at the critical pressure of around 0.8 GPa.We combine the first-principles calculations and k · p methods to discuss different types of strains induced topolog-ical phase transitions of both the ambient-pressure and high-pressure phase of Na₃Bi in detail.Our results indicates that symmetry plays a very important role on the topo-logical states.Especially,nonsymorphic space groups and nonsymorphic symmetry protected topological states push the study of topological phases into a climax in the recent years.Therefore,in the second part,we propose that the trigonal YH₃?Space Group:P???cl?at ambient pressure is a node-line semimetal protected by the glide sym-metry when spin-orbit coupling?SOC?is ignored,using ab initio calculations based on density-functional theory and effective model analysis.When SOC is included,a small gap?? 3 meV?appears,which leads YH₃ to be a strong topological insulator with Z₂ indices?1,000?.The corresponding surface states are somehow unique,and may be helpful to identify the real ground state of YH₃ in the experiment in the future.In the third part,we propose that the orthorhombic AgF₂?Space Group:Pbca?represents rich band-crossing features due to native nonsymmorphic symmetries in this system,Such as nodal surfaces,nodal lines and hourglass Dirac loops.We have found the above-mentioned band crossings are somehow isotropic,due to the permutation of the symmetries in this system.More interesting,we report the existence of the novel nodal chain and nodal armillary sphere penetrating the BZ?Brillouin zone?in this authentic material.The thesis is organized as the following:In chapter one,we first give a brief review of topological phases,from quantum hall effects to topological insulators,then from topological insulators to topological semimetals.We then emphasize on the fundamental properties of Weyl semimetals,in-cluding the original definition,the formation condition,the stability and Fermi-arc sur-face states of them.Then we give examples of the most popular topological semimetals,i.e.,the node-line semimetals and then discuss the stability and corresponding topolog-ical classification of them.Chapter two introduces the fundamentals of the the first-principles calculations,the representation theory of the space group and the k · p methods based on them.In chapter three,we investigate stress/strain induced quantum topological phase transition of Na₃Bi,a native 3D Dirac semimetal.Crystal-structure searching and dy-namic calculations afterwards show that pressure will induce a structural phase tran-sition of Na₃ Bi from the ambient P???c1 phase to cubic phase in the space group of Fm???m at the critical pressure around 0.8 GPa.The Luttinger model justify that the high-pressure phase is a isotropic massive Dirac semimetal without any topological characters.Then we discuss the effect about symmetry-broken induced decoupling of the irreducible representations on the model Hamiltonian,which justify that uniax-ial strain along the<001>direction can tune the high pressure Fm???m Na₃Bi from the parabolic semimetal into a Dirac semimetal,while shear strain along both the<100>and<111>directions can tune the high pressure Fm???m phase from the parabolic semimetal into a topological insultor.At last,we calculated surface states of Fm???m Na₃Bi based on the tight binding model constructed by the Wannier functions without strain and with different types of strains to verify these topological transitions.In chapter four,using ab initio calculations based on density-functional theory and effective model analysis,we propose that the P???c1 YH₃ is a node-line semimetal pro-tected by the glide-mirror symmetry when spin-orbit coupling is ignored.It's the band inversion of ?Y⁺,d_xz>and ?H1^-,s>orbits at ? point responsible for the formation of the nodal lines,and there are three nodal rings related to each other by the R₃z sym-metry.When SOC is included,a small gap?? 3 meV?appears,which leads YH₃ to be a strong topological insulator with Z₂ indices?1,000?.We find the surface states of this P3c1 phase are somehow unique and may be helpful to identify the real ground state of YH₃ using the angle-resolved photoemission spectroscopy?ARPES?technique in the experiment.In chapter five,we propose that the orthorhombic AgF₂?Space Group:Pbca?possess rich band-crossing features due to native nonsymmorphic symmetries in this system.We find that this system is very unique,all band crossings including nodal surfaces,nodal lines,hourglass Dirac loops are ternary due to the permutation of the symmetries in this system.Further more,we first report the existence of the novel nodal chain and nodal armillary sphere penetrating the BZ?Brillouin zone?in this authentic material.According to the bulk-boundary relation,we have calculated the surface states to justify these bulk nodal phenomena.Our results open the door to an unknown class of topological matters,and provide a platform to explore the corresponding intriguing physics.We conclude concisely and give some future prospects of topological semimetal in chapter six.