Ideal type-III nodal-ring phonons

Type-III nodal ring associated with a flat band without dispersion, whose nodes are the critical states between type-I and type-II Dirac/Weyl nodes, is of great interest. Here, we propose a strategy to explore and design materials that can realize the type-III nodal-ring phonons by introducing two-dimensional (2D) lattices with ideal flat band. As a concrete example, we show by first-principles calculations that the Laves phase $A{B}_{2}$ with $C14$ structure possesses ideal type-III nodal-ring phonons. The flat phonon band related to type-III nodal-ring phonons originates from their 2D triangular and kagome layers in the Laves phase $A{B}_{2}$. The type-III nodal-ring phonons with nontrivial Berry phase lie on a reflection-invariant plane, which are protected by the inversion and time-reversal symmetries. In addition, the drumhead surface states and unique surface arcs are clearly visible, which facilitate experimental observations. Our work enriches the classification of topological quantum phases, and provides a feasible strategy in designing flat-band related topological phases.