Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory

TL;DR

This paper develops a formalism to restore topological invariants in a driven non-Hermitian ladder system, addressing challenges posed by symmetry breaking and skin effects, and explores various driving protocols and their impact on topological phases.

Contribution

It introduces a generalized Brillouin zone approach to recover topological invariants in non-Hermitian Floquet systems with broken chiral symmetry, analyzing different driving protocols.

Findings

Delta and harmonic drives induce unidirectional skin effects.

Step drive can cause bi-directional skin effect.

Critical points without skin effect separate different localization regimes.

Abstract

In this paper, we study a non-Hermitian (NH) ladder subjected to a variety of driving protocols. The driven system looses chiral symmetry (CS) whose presence is indispensable for its topological characterization. Further, the bulk boundary correspondence (BBC) gets adversely affected due to the presence of non-Hermitian skin effect (NHSE). Here, we present a formalism that not only retrieves the lost CS, but also restores the BBC via the construction of a generalized Brillouin zone (GBZ). Specifically, we employ delta and step drives to compare and contrast between them with regard to their impact on NHSE. Further, a widely studied harmonic drive is invoked in this context, not only for the sake of completeness, but its distinct computational framework offers valuable insights on the properties of out-of-equilibrium systems. While the delta and the harmonic drives exhibit unidirectional skin effect in the system, the step drive may show bi-directional skin effect. Also, there are specific points in the parameter space that are devoid of skin effect. These act as critical points that distinguish the skin modes to be localized at one boundary or the other. Moreover, for the computation of the non-Bloch invariants, we employ GBZ via a pair of symmetric time frames corresponding to the delta and the step drives, while a high-frequency expansion was carried out to deal with the harmonic drive. Finally, we present phase boundary diagrams that demarcate distinct NH phases obtained via tracking the trajectories of the exceptional points. These diagrams demonstrate a co-existence of the zero and $\pi$ energy modes in the strong NH limit and thus may be relevant for studies of Floquet time crystals.