Coexistence of different dimensional topological states in stable ternary compound PrSbPt

Superconductivity in Mo–P compounds under pressure and in double-Weyl semimetal Hex-MoP2

“…Since the Weyl semimetals (WSMs) [1][2][3] were proposed in the TaA class, [4][5][6][7] they have attracted much attention due to their novel properties and enormous potential applications. Among these materials, the time-reversal or inversion symmetry has to be broken to guarantee the existence of Weyl points (WPs).…”

Coexistence of zero-, one- and two-dimensional degeneracy in tetragonal SnO$_2$ phonons

“…Before closing, note the following: (i) This study for the first time, to the best of our knowledge, reports that realistic SnO 2 [49] simultaneously hosts zero-dimensional TDP and DP phonons, one-dimensional WNLs phonons and two-dimensional nodal surface phonons. Although some previous studies proved that zero-, one-and twodimensional degeneracy coexisted in some electronic systems [46][47][48], not all the zero-, one-and two-dimensional topological elements were located at or around the Fermi level. Some additional technologies [47], such as hole or electron doping method, should be used to tune the topological elements to the Fermi level.…”

“…Although three types of fermions (i.e., zero-, one-, twodimensional degeneracy) have been proposed before in some electronic systems [46][47][48], they do not belong to the ideal candidate materials as the proposed topological elements are not near the Fermi level. As discussed above, in contrast to electronic systems, phonons are not limited by the Pauli exclusion principle, and thus, the entire frequency range of the phonon dispersion can be physically observed and used to search for topological elements.…”

“…The topological phonons proposed herein do not follow the limitations of the Pauli exclusion principle, and therefore, these topological phonons can be physically observed in the entire range of the phonon frequencies. (ii) The zero-, one-and two-dimensional topological elements coexist in some electronic systems, and their degenerate electronic structures are usually broken by the effect of spin-orbit coupling (SOC) [46]. However, the phonons, without SOC, provide us a new platform to search for material samples with true zero-, one-and two-dimensional topological elements in their phonon dispersion.…”

An ideal Weyl nodal ring with a large drumhead surface state in the orthorhombic compound TiS2

“…Based on different criteria, [29][30][31][32][33][34] topological states in metals or semimetals can be classified into different types such as nodal points, [35][36][37][38][39] nodal lines [40][41][42][43][44][45][46][47][48][49][50][51] and nodal surface states 31,32,[52][53][54][55][56] which can be distinguished from the band crossing dimensionality; Weyl, 1,[57][58][59][60] triple, [61][62][63][64][65] Dirac, 38,60,[66][67][68][69][70][71] sextuple 72 and octuple 21 states can be di...…”