Higher-order topological rainbow effect in non-Hermitian acoustic Kagome structures

A significant paradigm shift in condensed matter physics has been precipitated by the emergence of higherorder topological insulators. We design a higher-order Kagome acoustic crystal incorporating balanced gain and loss factors, thereby emulating non-Hermitian characteristics. This system exhibits the coexistence of two distinct corner states localized at the same angular positions within a supercell composed of two triangular domains with different topological phases, and the radius of one cylinder can control the frequency of the corner state. By constructing a polygonal structure formed by the expanded and shrunk lattices with distinct topological phases, we theoretically demonstrate that acoustic waves of various frequencies can be selectively trapped at a series of specific angles of this polygon. Moreover, these corner states are locked to the corner order, corresponding to the clockwise or anticlockwise orientation of the polygon, which leads to the higher-order topological rainbow. This work opens a new avenue for guiding and trapping multi-frequency acoustic energy, with potential applications in advanced acoustic devices.