Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems

TL;DR

This paper establishes a comprehensive topological bulk-boundary correspondence and classification for non-Hermitian nonlinear-eigenvalue systems, revealing exotic phases resulting from the interplay of non-Hermiticity and nonlinearity.

Contribution

It introduces an auxiliary system approach to restore the bulk-boundary correspondence and characterizes new complex-band topological phases in non-Hermitian nonlinear systems.

Findings

Restores bulk-boundary correspondence using generalized Brillouin zone.

Discovers coexistence of real-band and complex-band topological phases.

Provides a foundation for exploring topological physics in metamaterials.

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 nonzero topological invariants in the bulk. Widespread 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.