Sixfold degenerate nodal-point phonons: Symmetry analysis and materials realization

Complex nodal structure phonons formed by open and closed nodal lines in CoAsS and Na2CuP solids

“…29 Compared to the large number of studies in the field of twodimensional (2D) and three-dimensional (3D) topological electronic materials, the research concerning 3D topological phononic materials has only been initiated in the past few years. Roughly, the topological phonons in 3D solids can be divided into nodal point phonons, [36][37][38][39][40][41][42][43][44][45] nodal line phonons, [46][47][48][49][50][51][52][53][54][55][56][57][58] and nodal surface phonons, [59][60][61][62] respectively, corresponding to zerodimensional (0D), one-dimensional (1D), and 2D phonon band degeneracies in the 3D Brillouin zone (BZ). Note that the types of nodal line phonons are more diverse than those of nodal points and nodal surface phonons.…”

Cubic Ca3I3P with ideal charge-two triple point

“…The current study of crystal topology has even been further extended to bosons, including phonons, photons, and magnons. Phonons [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] can be a perfect platform for realizing these quasiparticles owing to their unique device applications and the advantages of whole frequency range observation. For example, in the phonon dispersion of three-dimensional-SiO 2 , Wang et al [40] proposed a topological triangular Weyl complex made up of one double Weyl point and two single Weyl points.…”

“…In realistic threedimensional materials with space group numbers 195-199, and 207-214, Liu et al reported charge-four Weyl point phonons. Xie et al [24] reported that sixfold degenerate nodal-point phonons could appear in three-dimensional materials C 3 N 4 , Sc 4 C 3 , Y 4 Sb 3 , and K 8 Si 46 . Chen et al…”

Ideal phononic charge-two nodal point and long nontrivial surface arcs in Na2Zn2O3

“…Recently, there has been great interest in exploring topological quasiparticles in phonons [1], which describe the atomic lattice vibrations in solids. So far, a number of materials hosting Weyl point phonons [2][3][4][5][6][7][8][9][10], Dirac point phonons [11,12], triple degenerate nodal point phonons [13,14], sixfold degenerate nodal point phonons [15,16], nodal line phonons [17][18][19][20][21][22][23][24][25][26][27][28][29][30] and nodal surfaces phonons [31][32][33] have been discovered. Compared with chiral fermions in electronic systems, chiral phonons exist without spin-orbital coupling.…”