Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits

TL;DR

This paper develops a Floquet non-Bloch formalism for non-Hermitian driven systems, revealing robust skin effects and topological edge states, and proposes a topolectrical circuit to experimentally observe these phenomena.

Contribution

It introduces a generalized Floquet non-Bloch framework for non-Hermitian systems, combining analytical derivations with experimental circuit design.

Findings

Skin effect persists across driving parameters

Low-frequency driving amplifies skin modes

Topolectrical circuits can simulate Floquet topological states

Abstract

Periodically driven systems intertwined with non-Hermiticity opens a rich arena for topological phases that transcend conventional Hermitian limits. The physical significance of these phases hinges on obtaining the topological invariants that restore the bulk-boundary correspondence, a task well explored for static non-Hermitian (NH) systems, while it remains elusive for the driven scenario. Here, we address this problem by constructing a generalized Floquet non-Bloch framework that analytically captures the spectral and topological properties of time-periodic NH systems. Employing a high-frequency Magnus expansion, we analytically derive an effective Floquet Hamiltonian and formulate the generalized Brillouin zone for a periodically driven quasi-one-dimensional system, namely, the Creutz ladder with a staggered complex potential. Our study demonstrates that the skin effect remains robust (despite the absence of non-reciprocal hopping) across a broad range of driving parameters, and is notably amplified in the low-frequency regime due to emergent longer-range couplings. We further employ a symmetric time frame approach that generates chiral-partner Hamiltonians, whose invariants, when appropriately combined, account for the full edge-state structure. To substantiate the theoretical framework, we propose a topolectrical circuit (TEC) that serves as a viable experimental setting. Apart from capturing the skin modes, the proposed TEC design faithfully reproduces the presence of distinct Floquet edge states, as revealed through the voltage and impedance profiles, respectively. Thus, our work not only offers a theoretical framework for exploring NH-driven systems, but also provides an experimentally feasible TEC architecture for realizing these phenomena stated above in a laboratory.