  Topological phases, including the conventional first-order and higher-order
topological insulators and semimetals, have emerged as a thriving topic in the
fields of condensed-matter physics and material science. Usually, a topological
insulator is characterized by a fixed order topological invariant and exhibits
associated bulk-boundary correspondence. Here, we realize a new type of
topological insulator in a bilayer phononic crystal, which hosts simultaneously
the first-order and second-order topologies, referred here as the hybrid-order
topological insulator. The one-dimensional gapless helical edge states, and
zero-dimensional corner states coexist in the same system. The new hybrid-order
topological phase may produce novel applications in topological acoustic
devices.
