  Topological phases of matter are classified based on their Hermitian
Hamiltonians, whose real-valued dispersions together with orthogonal
eigenstates form nontrivial topology. In the recently discovered higher-order
topological insulators (TIs), the bulk topology can even exhibit hierarchical
features, leading to topological corner states, as demonstrated in many
photonic and acoustic artificial materials. Naturally, the intrinsic loss in
these artificial materials has been omitted in the topology definition, due to
its non-Hermitian nature; in practice, the presence of loss is generally
considered harmful to the topological corner states. Here, we report the
experimental realization of a higher-order TI in an acoustic crystal, whose
nontrivial topology is induced by deliberately introduced losses. With local
acoustic measurements, we identify a topological bulk bandgap that is populated
with gapped edge states and in-gap corner states, as the hallmark signatures of
hierarchical higher-order topology. Our work establishes the non-Hermitian
route to higher-order topology, and paves the way to exploring various exotic
non-Hermiticity-induced topological phases.
