LAUSR

Based on first-principles calculations, we predict that the superconductor ${\mathrm{MgB}}_{2}$ with an ${\mathrm{AlB}}_{2}$-type centrosymmetric lattice hosts the so-called phononic topological Weyl nodal lines (PTWNLs) in its bulk phonon spectrum. These PTWNLs can be viewed as countless Weyl points (WPs) closely aligned along the straight lines in the $\ensuremath{-}H--K--H$ direction within the three-dimensional Brillouin zone (BZ) and are always paired with opposite Berry phase. Their topologically nontrivial natures are confirmed by the calculated Berry curvature distributions on the planes perpendicular to these lines. These lines are unique, because they are located exactly at the high-symmetry boundary of the BZ protected by the mirror symmetry and, simultaneously, are straightly transverse to the whole BZ, differently from known classifications, including nodal rings, nodal chains or nets, and nodal loops. On the $(10\overline{1}0)$ crystal surface, the PTWNL-induced drumhead-like nontrivial surface states appear within the rectangular area confined by the projected lines of the PTWNLs. Moreover, when the mirror symmetry is broken, the double-degenerate PTWNLs are further lifted to form a pair of WPs with opposite chirality. Our results pave the way for future experimental study of topological phonons on ${\mathrm{MgB}}_{2}$ and highlight similar results in a series of isostructural ${\mathrm{AlB}}_{2}$-type metallic diborides.