Theoretical Study On Phonon Topology Of Points And Surfaces In Solid Materials

In recent years,the rapid development of topological phonon materials has attracted the attention of many researchers.Compared with traditional topological electronic materials,phonon topological materials show several different characteristics.First,the Pauli exclusion principle has no limit.Second,due to thermal excitation,every boson subject to bochro-Einstein statistics will be relatively active.Meanwhile,bosons are not directly affected by electric and magnetic fields,so the study of topological phonon materials can study all phonon branches.For the newly emerging topological phonon materials,there are still few studies,especially the systematic study of the mechanism of the emergence of the same type of topological state is still relatively lacking,which leads to people’s blind and random search for topological phonon materials.Therefore,it is necessary to systematically study the same type of topological states in topological phonon materials,which is of great guiding significance both experimentally and theoretically.Therefore,starting from the lattice symmetry protection,we screen the target topological states in the 230 mid-space group,and find the real materials for theoretical calculation.Based on the first principles and Wanier function,this paper systematically studies the highest devolution degree of topological phonon system-six degenerate points,explains the formation mechanism of the six degenerate points from the point of symmetry,and on this basis continues to look for the possibility of coexistence of multiple degenerate points,at the same time systematically studies the highest dimension of topological phonon system-nodoplane,and continues to improve the study of nodoplane.Finally,we look for coexistence and compensation between points and surfaces.More specific studies are as follows:First,we screened the space groups with possible hexadecimal degeneracy points from230 kinds of space groups,and found five space groups with possible hexadecimal degeneracy points.Their space groups are 218,220,222,223 and 230,respectively.In addition,some materials are found in these space groups for theoretical calculation.It can be seen that there are six emphases at the H point of C₃N₄,Sc₄C₃and Y₄Sb₃of space group 220in the frequency range of 36-37 THz,15.52-15.62 THz and 4.97-5.00 THz respectively.Other space groups（such as 218,222,223）have six emphases at point R,and space group 230 has six emphases at point H.At the same time,we select some materials and calculate their surface states.We can see two clear Fermi arcs coming from the six degenerate points.Such a clean surface state without body occlusion will be helpful for experimental observation.At the same time,we discuss the mechanism of the six degenerate points in theory,and give the effective Hamiltonian with six degenerate points in the five space groups,and prove that the appearance of six degenerate points is protected by lattice symmetry.We systematically study the six degenerate production mechanisms,which will be of great significance for sorting out topological phonon materials.For example,we look for other multiple degeneracy points on the basis of the existence of six degeneracy points.We find that Ta3Sn in space group 223 not only has six degeneracy points,but also has three degeneracy points and four degeneracy points.We find that different from the six degeneracy points,the three degeneracy points and four degeneracy points have quadratic type dispersion.This greatly enriches the topological types of phonon materials,and clear surface states are helpful for laboratory observation.Secondly,on the basis of the study of single plane,we studied the two-node plane and three-node plane.We also conducted structural search in 230 kinds of space groups,and found that 19 kinds of space groups have two-node plane,and the other 9 kinds of space groups have three-node plane.We gave the symmetry conditions of two-node plane and three-node plane,and found the corresponding real materials in these 28 kinds of space groups.You can see that there are indeed two-and three-node surfaces in these materials.It proves that we are right to analyze the mechanism of nodal plane existence theoretically.At the same time,we find that there may be some other topological states in these nodes.For example,double-nodal and three-nodal surfaces appear in the square Brillouin region.At this time,the double-nodal and three-nodal surfaces will have a common high symmetric boundary,so it is possible to have a quadruple degenerate nodal line—Dirac nodal line.For the three-nodal surface,there will be more Dirac lines,so as to form a Dirac nodal line network.At the same time,we also mention that due to the restriction of no-go theorem,isolated Weil points may appear in the three-node plane.Finally,we study the interdimensional topological states in which 0-dimensional points and 2-dimensional surfaces coexist and compensate each other.Research in the magnetic spin system single foreign section point,and the coexistence,the foreign,single point can carry the same and without any chiral（C（28）1）.First,we screened 230 kinds of space groups for the existence of inversion symmetry,among which 138 space groups met the requirements.Based on this,we screened for the existence of nodal planes,and classified them according to single nodal planes,double nodal planes and three nodal planes.Then,in these space group screening,there may only exist Weyl points without any chirality,and it is found that only under the single node plane can there be a qualified space group.We find two real materials in these space groups for theoretical calculation and proof.Zr₃O in two kinds of material and can be observed in the phonon spectrum of Na PH₂NO₃C（28）1 single external points,both from the state of plane and bell curvature distribution can be seen outside of the point and surface compensation phenomenon happened.Our findings apply to many spin-free systems,including phonons,other bosons,and even electronic systems without spin-orbital coupling.