Two-dimensional topological insulators for first order and higher order, characterized respectively by in-gap edge states and corner states, have attracted tremendous research interest. Different from them, two-dimensional topological metals exhibit topological boundary states in the absence of bulk bandgaps. While first-order topological metals with anti-chiral or anti-helical edge states have been implemented, higher-order topological metals still lack systematic experimental investigation. Here, we propose a practically accessible approach to two-dimensional higher-order topological metals and demonstrate their experimental realization in phononic crystals. The metallic bulk states, gapped anti-helical edge states, and topological corner states, are unambiguously demonstrated via airborne sound experiments. As the key feature of such topological metal, the topological corner states are embedded in the continuous spectrum of metallic bulk bands, namely the bound corner states in the continuum. Our findings evidence higher-order topological states in metallic phases, and may promote the development of next-generation devices for acoustic wave manipulation. Higher-order topology has been well established in insulators and semimetals. Here, authors evidence higher-order topology in metallic systems, and unveil a type of topological corner states that are naturally embedded in the bulk continuum with no need for intentional engineering.
Chen et al. (Wed,) studied this question.