Arbitrary geometric path transport based on topological acoustic alloys

Symmetry-protected topological edge states of acoustic metamaterials offer an unprecedented prospect for guiding and manipulating sound waves. However, these conventional boundaries—conventionally constructed between crystals of distinct topological phases—are inherently limited by crystalline symmetry requirements (e.g., spin-momentum-locked edge states). Here, by randomly doping an acoustic semimetal with topological or ordinary phases at varying concentrations, we realize a class of aperiodic metamaterials, termed acoustic topological (ordinary) alloys in time-reversal symmetric systems. Such an alloy inherits the topological (ordinary) property of doped elements, where the native topological invariant and acoustic pseudospins remain unchanged. We demonstrate that the boundaries formed by such topological alloys are no longer constrained by crystalline symmetry, enabling robust transmission along arbitrary paths. Finally, we demonstrate a tunable multi-port power divider and an acoustic topological logic gate based on acoustic alloys. Our findings eliminate the geometric constraint on the topological boundary shape, offering a versatile platform for on-demand wave control along irregular and arbitrary paths.