Robust Zero Modes in Non-Hermitian Systems without Global Symmetries

Authors

Jose D. H. Rivero, CUNY College of Staten IslandFollow
Courtney Fleming, CUNY College of Staten IslandFollow
Bingkun Qi, CUNY College of Staten IslandFollow
Liang Feng, University of Pennsylvania
Li Ge, CUNY College of Staten IslandFollow

Document Type

Article

Publication Date

11-29-2023

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.

Comments

This article was originally published in Physical Review Letters, available at https://doi.org/10.1103/PhysRevLett.131.223801