Characterizing non-Hermitian topological monomodes via fractional mode charges in acoustic systems

Non-Hermitian properties play an important role in topological acoustic systems, which can not only change the band topology but may also lead to novel applications such as non-Hermitian skin effect (NHSE). However, non-Hermitian systems, which are more closely related to real-world systems due to inevitable losses or gains, present challenges to topological classifications and boundary correspondence. Here, we demonstrate a topological monomodes based on one-dimensional (1D) Su−Schrieffer−Heeger (SSH) chains subject to non-Hermitian loss influences, which is achieved through tuning and introducing loss in the coupled acoustic cavity system. Moreover, we have extended this phenomenon from low-dimensional to high-dimensional systems. Theoretical and simulation results indicate that monomode can still be observed in non-Hermitian acoustic high-dimensional models, challenging the notion that topological states can only occur in pairs. More importantly, we have simulated the acoustic topological monomodes under non-Hermitian high-dimensional systems using acoustic local density of states (LDOS). Theoretical and simulation results demonstrate that local density of states can be used to calculate fractional charge modes and characterize topological monomodes in non-Hermitian acoustic systems. Our findings may have significant implications for the characterization of topology in non-Hermitian acoustic systems. This discovery offers a new perspective and approach to the study of non-Hermitian acoustic topology.