Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems

• URL: http://arxiv.org/abs/2511.13076v1
• Date: Mon, 17 Nov 2025 07:25:17 GMT
• Title: Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Authors: Yu-Peng Ma, Ming-Jian Gao, Jun-Hong An,
• Abstract summary: We establish a complete BBC and topological characterization of the topological phases in a class of non-Hermitian nonlinear-eigenvalue systems.<n>Remarkably, we discover that the interplay between non-Hermiticity and nonlinearity creates an exotic complex-band topological phase.<n>Our results enrich the family of nonlinear topological phases and lay a foundation for exploring novel topological physics in metamaterial systems.
• Score: 0.6933020649563102
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of boundary states with non-zero topological invariants in the bulk. A wide attention has been paid to extending topological phases to nonlinear and non-Hermitian systems. However, the BBC and topological invariants of non-Hermitian nonlinear systems remain largely unexplored. Here, we establish a complete BBC and topological characterization of the topological phases in a class of non-Hermitian nonlinear-eigenvalue systems by introducing an auxiliary system. We restore the BBC broken by non-Hermiticity via employing the generalized Brillouin zone on the auxiliary system. Remarkably, we discover that the interplay between non-Hermiticity and nonlinearity creates an exotic complex-band topological phase that coexists with the real-band topological phase. Our results enrich the family of nonlinear topological phases and lay a foundation for exploring novel topological physics in metamaterial systems.

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