Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems

TL;DR

This paper explores how gain and loss in non-Hermitian Floquet systems induce multiple topological phase transitions and spectral singularities, revealing new boundary modes and anomalous transmission phenomena with potential experimental applications.

Contribution

It uncovers two novel phenomena: topological transitions among Floquet insulators caused by gain/loss, and spectral singularities leading to anomalous transmission in non-Hermitian Floquet systems.

Findings

Multiple topological phase transitions induced by gain and loss.

Hybrid skin-topological boundary modes with unique localization properties.

Spectral singularities causing anomalous transmission at flat bands.

Abstract

The interplay between Floquet driving and non-Hermitian gain/loss could give rise to intriguing phenomena including topological funneling of light, edge-state delocalization, anomalous topological transitions and Floquet non-Hermitian skin effects. In this work, we uncover two unique phenomena in Floquet systems caused by gain and loss. First, multiple topological transitions from anomalous Floquet second-order topological insulators to anomalous Floquet first-order topological insulators and then to normal insulators can be induced by gain and loss. Interestingly, the resulting anomalous Floquet insulators further carry hybrid skin-topological boundary modes, which could either be fully localized or localized to different edges at different time slices and traversing along all edges in a single driving period. The topological phase transitions are also shown to be detectable through studies of transmission properties in the setting of coupled ring resonators. Second, gain and loss are found to induce singularities in the Floquet spectral, around which anomalous transmissions at flat quasienergy bands are predicted. These discoveries not only enhanced our understanding of topological matter and phase transitions in driven non-Hermitian systems, but also promoted their experimental realizations in optical and acoustic settings.