  Higher-order topological insulators exhibit multidimensional topological
physics and unique application values due to their ability of integrating
stable boundary states at multiple dimensions in a single chip. However, for
signal-processing applications in high-frequency mechanical systems, the
current realizations of higher-order topological mechanical materials are still
limited to large-scale systems for kilohertz or lower frequencies. Here, we
report the experimental observation of a on-chip micromechanical metamaterial
as higher-order topological insulator for high-frequency mechanical waves. The
higher-order topological phononic band gap is induced by the band inversion at
the Brillouin zone corner which is achieved by configuring the orientations of
the elliptic pillars etched on the silicon chip. With consistent experiments
and theory, we demonstrate the coexistence of topological edge and corner
states in the megahertz frequency regime as induced by the higher-order band
topology. The experimental realization of on-chip micromechanical metamaterials
with higher-order topology opens a regime for applications based on megahertz
mechanical waves in an integrated platform where the edge and corner states act
as stable waveguides and resonators, respectively.
