First-principle Calculations On Topological Materials

"Ten-fold way" topological classification table tells us that different spatial dimen-sions and symmetries correspond to different topological classes.However,this table only contains time-reversal symmetry,particle-hole symmetry can chiral symmetries,and not only a crystalline symmetry.Discoveries for topological insulators,topologi-cal crystalline insulators,and high-order topological insulators make people realize that crystalline symmetries can bring new topological states and the diversity of symmetry-protected topological states in materials.Thus classification of topological states for the variety of crystalline symmetries becomes a vital issue.Inspired by Fu-Kane formula,two individual groups from Princeton and Harvard found that topological information is included at several high-symmetry points in the Brillouin zone.They both pointed out that a system is topologically nontrivial if it can not adiabatically evolve into an atomic insulator,but use different methods to classify topological states in 230 space groups.The research group from Harvard told us that topological classes for 230 space groups are isomorphic to some Abelian groups,which is called symmetry-based indicators.One of my work in this thesis is to explain the topological information and explicit formula for the symmetry-based indicators in the presence and absence of spin-orbit coupling.Later,we use the symmetry-based indica-tor formulas and first-principle calculations to implement a high throughput calculation for electronic materials and catalog almost 9000 topological materials.All the data are searchable and available at http://materiae.iphy.ac.cn.With the development of topological band theory,researches for topological states has been studied not only in electronic systems but also in bosonic systems,such as phonons,photons,magnon and so on.Another work shown in this thesis is the topolog-ical study for MSi transition-metal monosilicides in phononic systems.We found two kinds of double-Weyl in the phonon spectra of MSi having 3-fold degeneracy and 4-fold degeneracy respectively,which is protected by time-reversal symmetry and crystalline symmetries.Those two kinds of double-Weyl points have verified by high-resolution inelastic X-ray scattering experiments.