Robust Zero Modes in Non-Hermitian Systems without Global Symmetries.

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.

Non-Hermiticity-Governed Active Photonic Resonances.

Photonic resonances play an essential role in the generation and propagation of light in optical and photonic devices, as well as in light-matter interaction, including nonlinear optical responses. Previous studies in lasers and other open systems have shown exotic roles played by non-Hermiticity on modifying passive resonances, defined in the absence of optical gain and loss. Here we report a new type of resonances in non-Hermitian photonic systems that does not originate from a passive resonance, identified by analyzing a unique quantization condition in the non-Hermitian extension of the Wentzel-Kramers-Brillouin method.

Pseudochirality: A Manifestation of Noether's Theorem in Non-Hermitian Systems.

Noether's theorem relates constants of motion to the symmetries of the system. Here we investigate a manifestation of Noether's theorem in non-Hermitian systems, where the inner product is defined differently from quantum mechanics. In this framework, a generalized symmetry that we term pseudochirality emerges naturally as the counterpart of symmetries defined by a commutation relation in quantum mechanics.