Topology and edge modes surviving criticality in non-Hermitian Floquet systems

TL;DR

This paper uncovers gapless symmetry-protected topological phases in non-Hermitian Floquet systems, revealing robust edge modes at critical points through a unified topological framework involving generalized Brillouin zones.

Contribution

It introduces a novel topological characterization of gapless SPTs in non-Hermitian Floquet systems using winding numbers and generalized Brillouin zones, extending topological analysis to critical points.

Findings

Identification of gapless SPTs in driven non-Hermitian systems.

Development of a unified topological framework using generalized Brillouin zones.

Discovery of robust edge modes at phase transitions beyond equilibrium.

Abstract

The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points. The theory is demonstrated in a broad class of Floquet bipartite lattices, unveiling unique topological criticality of non-Hermitian Floquet origin. Our findings identify gSPTs in driven open systems and uncover robust topological edge modes at phase transitions beyond equilibrium.