  We demonstrate that HOTIs with the quantization of the quadrupole moments can
be realized in the two-dimensional elastic phononic crystals (PnCs). Both
one-dimensional (1D) topological edge states and zero-dimensional (0D)
topological corner states are visualized and can be transformed each other by
tuning the crystalline symmetry in a hierarchical structure. The systematic
band structure calculations indicate that elastic wave energy in the
hierarchical structure can be localized with remarkable robustness, which is
very promising for new generations of integrated solid-state phononic circuits
with a great versatility.
