Excitation of maximal degeneracy and higher-order topology in phononic crystals

Since the discovery of the Weyl fermion in the material $\mathrm{Ta}\mathrm{As}$, searching for new types of (quasi)particles in the universe of condensed matter and materials, beyond those captured in the real universe, has aroused tremendous interest. More recently, an exotic excitation, of linear dispersion and up to sixfold degeneracy, has been predicted theoretically in a three-dimensional material, which harbors hinge arc states on the boundary thus manifesting a nontrivial higher-order topology. The sixfold excitations, with the maximal degeneracy or degree of freedom of bosons, may open up an opportunity for exploring the extraordinary properties of topological matter such as three-dimensional robust one-way transport. However, such states have not been explored experimentally in any classical systems. In this work, we report the experimental realization of the sixfold excitation in a three-dimensional phononic crystal. We reveal that the linear sixfold excitation can be decomposed as two overlapping threefold spin-1 Weyl points with opposite topological charges \ifmmode\pm\else\textpm\fi{}2. We further demonstrate the hinge arc states associated with the excitation, which are featured with the longest hinge arc, revealing the higher-order topological nature of the material.