Robust zero modes in non-Hermitian systems without global symmetries

TL;DR

This paper introduces a method to create robust zero modes in non-Hermitian lattice models without relying on symmetry or topology, demonstrating their formation, properties, and potential photonic realizations.

Contribution

The authors develop a symmetry-free approach to generate zero modes in non-Hermitian systems, expanding the understanding of topological-like states beyond traditional symmetry-based frameworks.

Findings

Zero modes can be formed by attaching a small cluster to the bulk, acting as a nucleus.

The approach is inherently non-Hermitian, requiring specific boundary-bulk couplings.

Photonic lattice experiments can observe these zero modes as single lasing modes.

Abstract

We present an approach to achieve zero modes in lattice models that do not rely on any symmetry or topology of the bulk, which are robust against disorder in the bulk of any type and strength. Such symmetry-free zero modes (SFZMs) are formed by attaching a single site or small cluster with zero mode(s) to the bulk, which serves as the "nucleus" that expands to the entire lattice. We identify the requirements on the couplings between this boundary and the bulk, which reveals that this approach is intrinsically non-Hermitian. We then provide several examples with either an arbitrary or structured bulk, forming spectrally embedded zero modes in the bulk continuum, midgap zero modes, and even restoring the "zeroness" of coupling or disorder-shifted topological corner states. Focusing on viable realizations using photonic lattices, we show that the resulting SFZM can be observed as the single lasing mode when optical gain is applied to the boundary.