Non-Hermitian-induced higher-order topological phases in acoustic fractal lattices
For fractal (non-integer-dimension) geometries in Hermitian system, high-order topological phases were realized in the past few years, for which, it is difficult to tune the energy concentration degree of topological states flexibly and smoothly. Non-Hermiticity method is expected to solve this problem. However, in non-integer-dimension system, the non-Hermitian-fractal coupled topological mechanism is unclear and topological phases induced by non-Hermiticity remain unrealized. By introducing a loss contrast in a fractal lattice, this study proposes a non-Hermitian route to realize higher-order topological phases in acoustic fractal lattices with good tunability. Based on the tight-binding approximation, calculations on the Hamiltonian of the system yield the wave-function distribution of the zero-energy modes, revealing the formation mechanisms and conditions for the topological phase transitions induced by non-Hermiticity in acoustic fractal lattices. We numerically and experimentally realize non-Hermitian-induced topological edge and corner states in a fractal structure. Furthermore, a tunable acoustic energy concentrator has been realized, namely, the degree of acoustic energy localization can be tuned conveniently by merely adjusting the loss contrast, rather than redesigning the structure parameters. This work not only establishes an effective mechanism for manipulating higher-order topology in complex fractal geometries through non-Hermiticity but also provides a theoretical framework for exploring exotic topological states of matter in non-integer dimensions.