First-principles Study Of Topological Phonon Materials

In recent years,topological materials have attracted great attention due to their novel phys-ical properties,which are topologically robust and have potential applications in electronic de-vices.At the beginning of the study,many efforts have been devoted into the topological clas-sification of insulators（or semiconductors）.For instance,the topological quantum states in the quantum Hall effect,which is a new classification mechanism beyond the famous Landau theory.Such classification is inspiring because the framework of spontaneous symmetry breaking has been successfully used for classifying quantum states in condensed matters for so many years.Following the research of the quantum Hall effect,topological insulators are proposed as the first type of intrinsic topological materials,which exhibit conductive topological surface states protected by the time-reversal symmetry when the bulk states are insulating.Shortly after the discovery of topological insulators,study focus have been slightly transferred to the topological semimetals since they provide an ideal platform for studying relativistic particles in condensed matter.In particular,the discoveries of Weyl/Dirac semimetals,in both two and three dimen-sions,tremendously accelerate the advancement of topological quantum states.Compared with the great advancement in topological fermions,in another important subject,i.e.,the bosonic systems,topological quasiparticles are rarely discussed.In particular,the topological phonon responses in the range of THz frequency,where the electron-phonon coupling and thermal trans-ports play important roles,are still in its infancy.Using first-principles method and symmetry analysis,we propose a recipe for explor-ing three-dimensional Dirac phonons in crystalline solids.The symmetry conditions for the existence of three-dimensional Dirac phonons were identified in all space groups with inver-sion symmetry.We prove that non-symmorphic symmetry and a combination of inversion and time-reversal symmetries play essential roles in the high degeneracy of three-dimensional Dirac phonons.Both the symmetry-enforced and accidental degeneracies are discussed as the coun-terparts of Bi O₂and Na₃Bi in electronic systems,respectively.We show that,three-dimensional Dirac phonons are more likely to be achieved in the symmetry-enforced case,which is different from the electronic systems.Space groups that satisfy the symmetry conditions are provid-ed.By performing first-principles calculations,we present two realistic materials,i.e.,Si（c I16）and Nb₃Te₃As,exhibiting Dirac-type dispersions and visible phonon surface states,as potential candidates for experimental examinations.To enlarge the classification of topological phonon quasiparticles,we theoretically demon-strate that a triangular Weyl complex can occur in topological phonon systems with trigonal or hexagonal lattices.The unpaired Weyl complex is protected to locate at high-symmetry points due to the screw rotational symmetry,which guarantees that surface arcs are extremely long and span the entire surface Brillouin-zone.These giant phonon arcs provide entire modes of topological surface states,suggesting many applications.More importantly,we identify by first-principles calculations that there are only nontrivial surface arcs across the iso-frequency surface in realistic candidates（i.e.,α-Si O₂and YPt₂B）,which greatly facilitate their detection in experiments and practical applications.We believe that our work will broaden the classification of topological phases and give further impetus to topological studies in bosonic systems.It is not only of great significance for searching topological phonon materials,but also contributing to the researches in phononic and photonic crystals.