Lasing zero modes are not always topological

Abstract The convergence of non-Hermitian physics and topology has inspired new ideas and applications across various physical platforms such as optics, electronics and acoustics. Despite these efforts, the interplay between non-Hermiticity and topology with nonlinear effects remains largely unexplored. Topological lasers exemplify this gap, where it is often assumed–without justification–that lasing zero modes inherit the spectral and spatial characteristics of their linear counterparts- an assumption that undermines the nonlinear interactions inherent in laser systems. Contrary to this, we show that the interplay between coupling rates, dissipation, and gain saturation nonlinearity in laser arrays can delocalize the otherwise localized linear topological states, signaling a breakdown of bulk-boundary correspondence. These findings, offer deeper insights into the intricate interplay between non-Hermiticity, topology, and nonlinear effects. They also suggest intriguing connections between many-body dissipative interactions and topology in open quantum systems.