Characterizing the non-Hermitian route to higher-order topology via fractional mode charges in acoustic systems

Non-Hermitian factors play a key role in introducing changes to the topology of acoustic systems, by significantly expanding the classification of topological phases beyond traditional Hermitian theory and presenting challenges to the conventional bulk–boundary correspondence. Traditional Hermitian theory cannot fully describe the complicated behavior of systems interacting with their environment, thus non-Hermitian theory emerged. Currently, most non-Hermitian topological systems derive their phases from Hermitian components, which entails concurrently considering the gain and loss of the system. In the study of higher-order topological insulators, higher-order topological states are usually achieved by modulating coupling strengths. While traditionally it is viewed that dissipation in topological systems is detrimental to the topological states, recent research studies have challenged this perspective. The nontrivial topology can arise by introducing loss of a specific configuration in a trivial phase. In this study, through finite-element simulations of coupled acoustic cavity systems from one-dimensional to three-dimensional structure, it is illustrated how intentionally introducing non-Hermitian loss can induce the higher-order topology. More crucially, we have simulated the acoustic local density of states (LDOS) and calculated fractional charge modes and can directly observe and prove through LDOS that introducing loss can convert a trivial system into a topological one. Both theoretical and simulated results show that the LDOS can be used to calculate fractional charge modes, effectively characterizing higher-order topological states in non-Hermitian acoustic systems. This study carves out a research pathway for the future of non-Hermitian acoustic topology.