First-Principles Calculations And Model Studies Of Topological Phononic Materials

In recent decades,topological electronic materials such as topological insulators,topological semimetals and topological superconductors have been widely studied.For electronic materials,the energy range that we can study is mainly around the Fermi level of the systems.As a result,physical properties far from the Fermi level are much difficult to observe experimentally.However,phonons formed by lattice vibrations do not have a Fermi surface,thus the physical properties in the entire energy region may be observed in experiments.In this thesis,we investigated the topological phonon properties of realistic materials,and uncovered several interesting topological phononic phononmena including phononic Dirac points,Weyl points,nodal lines,and nodal surfaces.The main research contents are shown in the following:?.We studied the classification and existence conditions of phononic topological open nodal lines in the coexistence of parity inversion and time-reversal symmetries,and found the realistic materials that are suitable for the corresponding classification.According to the model analysis,we divited the open nodal lines into three types:"O-shape"open nodal lines(Type-I),"X-shape"open nodal lines(Type-II)and“straight-line-shape"open nodal lines(Type-III).We found that Rb₂Sn₂O₃can form the Type-I open phonon nodal lines in No.166space group.In phonon spectrum of Rb₂Sn₂O₃,we found that there are gapless points protected by two different irreducible representations along the paths?-X and L-B₁ near to5.6 and 18.5 THz.The numerical calculations by using surface Green's function show that the(010)suface of Rb₂Sn₂O₃ can form perfect drumhead-like surface states.At the same time,Fermi arcs and Type-I open phonon nodal lines dispaly isosurfaces with different frequencies.In addition,we also found that the phonon spectrum of Mg B₂(space group 191)could form Type-III open nodal lines.?.Taking the Rb Te Au family material in space group 51 as an example,we systematica--lly studied the topological properties of phonon nodal surfaces.In the phonon dispersion of Rb Te Au family of materials,we found that double-degenerate flat bands are formed along the highly symmetrical paths S-Y and R-T.Moreover,these flat bands dispaly nodal surfaces in the first Brillouin zone.To perform a further investiagation,we found that there is an integer?jump in the Berry phase along the?-S-Y path,and there is linear singularities in the Berry curvature.On the(001)surface,we found the Dirac cone.On the(010)surface,bulk states can be observed because the nodal surfaces are projected into the Brillouin zone of the(010)surface.It is a great significance for us to understand the formation and topological properties of topological phonon nodal surfaces.?.Taking the semiconductor Cu Cl as an example,we systematically study the topologi--cal properties of topological phonon nodal links and multiple degenerate nodal lines.We found that the phonon dispersion of Cu Cl has some gapless points along the high symmetry paths?-X and M-?,which form nodal links near to 5.1 THz and the drumhead-like surface states on the(001)and(110)surfaces.We found that Berry phase has a jump with an integer?and Berry curvature dispalys as a ring shape,which confirms further the topological properties of the node link.Quadruple degenerate nodal lines could be formed along the high symmetry path R-M of the phonon spectrum.In addition,these points form an open quadruple degenerate node line state at the boundary of the BZ.The Dirac cone can be formed on(001)surface.Nodal links and multiple degenerate node-lines can coexist in the same material,which is helpful to understand the topological properties of topological phononic nodal links and node lines.?.For the chiral space group,we fondd that there are monopole Weyl points protected by symmetry at certain determined high symmetry points,such as single Weyl points,spin-1Weyl points and so on in the acoustic systems.In 230 space group,we firstly screen the high symmetry points of the space group with all double degenerate points,triple degenerate points,or quadruple degenerate points through the irreducible repesentations.Then we delete the space group with spatial inversion,mirror symmetry or improper symmetry.At last,the space groups with symmetry-protected Weyls can be selected.We searched six space groups:W points of space groups 24 and 210,and P points of space groups 80,98,199,and 214.?and H points of space groups 199 and 214 have the spin-1 Weyl points.In space group 199,we found that the left-hand chirality Weyl points at P1 and P2 points of K₂Sn₂O₃,which are the monopole Weyl points;at H point,we firstly found there are spin-1 Weyl points which are not affected by the LO-TO splitting in the acoustic systems.On the(001)and(110)surfaces,we found that there are the double-helicoid surface states and a clearly visible large phononic Fermi arc.