Lasing zero modes are not always topological

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. The interplay between gain saturation, nonlinearity, and band topology is investigated in SSH laser arrays. The authors show that, in certain regimes, the lasing zero mode no longer inherits the spatial profile of the localized defect state dictated by the underlying topological lattice. Instead, it becomes delocalized, with its intensity distributed nearly uniformly across the entire array.