Phononic Weyl Nodal Straight Lines in High-Temperature Superconductor MgB$_2$

Abstract

Based on first-principles calculations, we predict that the superconducting MgB 2 with a AlB 2 -type centrosymmetric lattice host the so-called phononic topological Weyl nodal lines (PTWNLs) on its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the −H-K-H direction within the three-dimensional Brillouin zone (BZ). Their topological non-trivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are highly unique, because they exactly locate at the high-symmetry boundary of the BZ protected by the mirror symmetry and, simultaneously, straightly transverse the whole BZ, in different from known classifications including nodal rings, nodal chains or nets, and nodal loops. On the (10 10) crystal surface, the PTWNLs-induced drumhead-like non-trivial surface states appear within the rectangular area confined by the projected lines of the PTWNLs with opposite chirality. Moreover, when the mirror symmetry is broken, the double-degenerate PTWNLs are further lifted to form a pair WPs with opposite chirality. Our results pave the ways for future experimental study on topological phonons on MgB 2 and highlights similar results in a series of isostructural AlB 2 -type metallic diborides.

Topology of triple-point metals*

“…The concept of topology from the electronic bandstructure has been successfully extended to the vibrational bandstructure of materials [89][90][91][92][93]. In recent works, topologically protected band-crossings have been reported in the phonon spectrum of solid state crystals [41,[94][95][96][97]. Soon after the theoretical prediction of double-Weyl phonons in the phonon spectrum of transition-metal monosilicides MSi (M=Fe, Co, Mn, Re, Ru) [94], Miao et al [98] experimentally reported the first observation of double Weyl points in FeSi by means of inelastic x-ray scattering measurements.…”

“…Recently, topologically protected Weyl nodal lines have been predicted in the phonon spectrum of bulk MgB 2 [97].…”

Ideal type-II Weyl phonons in wurtzite CuI

“…Since the theoretical prediction and experimental realization of Weyl semimetal state in the TaAs class of compounds [1][2][3][4], Weyl materials including Weyl fermions [5][6][7][8][9][10][11][12], Weyl photonic crystal [13,14] and Weyl phononic crystal [15][16][17][18][19][20] with novel surface states have attracted significant interest recently. The spin-1/2 Weyl points (WPs) emerging in solids without time reversal symmetry or inversion symmetry are the twofold degenerated crossing points of two linearly dispersing bands in the three directions of momentum space [21,22].…”

Topological Weyl-like Phonons and Nodal Line Phonons in Graphene

“…Therefore, all these four crossing points of PW1, PW2, PW3, and PW4 are phononic Weyl-like points. It needs to be emphasized that the general Weyl point is in the 3D conical shape [23], as already emphasized in many electronic Weyl semimetals and several phononic Weyl materials [56][57][58][59][60][61][62]. However, given the fact that it is not physically allowed for any 3D shape for graphene due to its single layer structure and the phononic band is spinless, it is reason- able to define these crossings as Weyl-like phonons.…”

“…Moreover, it needs to be emphasized that for PW4 no edge states can be clearly observed because the PW4-induced topologically protected phononic edge states fully overlap with the edge projection from the phonon dispersions of the pristine graphene. In the third, in similarity to the nodal lines in 3D crystals which exhibits nontrivial drumhead-like surface states for BaSn 2 , Ca 3 P, TlTaSe 2 and TiSi, ZrSiS [63][64][65][66][67] and the phononic Weyl nodal line MgB 2 [60], the existence of PNL of the pristine graphene at 24.38 THz induces the straight-line edge states, simultaneously, with an arc-like going-downwards parabola in its frequencies upon the q momentum, as shown in Fig. 4(d).…”