  The higher-order topological insulators (HOTIs), with such as the topological
corner states, emerge as a thriving topic in the field of topological physics.
But few connections have been found for the HOTIs with the well explored
first-order topological insulators described by the Z_2 index. However, most
recently, a proposal asserts that a significant bridge can be established
between the HOTIs and the Z_2 topological insulators. When subject to an
in-plane Zeeman field, the corner states, the signature of the HOTIs, can be
induced in a Z_2 topological insulator. Such Zeeman field can be produced, for
example, by the ferromagnetic proximity effect or magnetic atom doping, which
obviously involves the drastically experimental complexity. Here we show that,
a phononic crystal, designed as a bilayer of coupled acoustic cavities, hosts
exactly the Kane-Mele model with built-in in-plane Zeeman fields. We observe
that the helical edge states along the zigzag edges are gapped, and the corner
states, localized spatially at the corners of the samples, appear in the gap,
confirming the effect induced by the Zeeman field. We further demonstrate the
intriguing contrast properties of the corner states at the outer and inner
corners in a hexagonal ring-shaped sample.
