Topological sound in nonreciprocal active-liquid networks

Recent advances in nonreciprocal topological networks have discovered a type of anomalous topological edge states with superior robustness against larger disorders than the quasienergy band gap. However, to date, all previously demonstrated nonreciprocal topological networks have required external drives such as magnetic fields or time modulation to break the time-reversal symmetry (TRS). Here, by extending this concept to topological active matter systems with spontaneous TRS breaking, we demonstrate robust acoustic anomalous and Chern edge states in a self-propelled nonreciprocal active-liquid network without any external drives. More interestingly, we show that the anomalous topological edge states exhibit superior robustness against Hermitian disorders even than the Chern ones. Furthermore, we discover that such superior robustness no longer holds in the presence of non-Hermitian perturbations, and both the anomalous and Chern edge states transition to the corner skin modes by the non-Hermitian skin effect. Our work extends the nonreciprocal topological networks to active matter and non-Hermitian systems, offering possibilities for sound manipulation in a highly unusual way.