Topological properties of a periodically driven Creutz ladder

TL;DR

This paper explores the topological phases of a periodically driven Creutz ladder under sinusoidal and delta-kick drives, revealing frequency-dependent topological transitions and the emergence of zero and pi energy modes.

Contribution

It introduces a detailed analysis of Floquet topological invariants in driven Creutz ladders, highlighting how different driving protocols affect edge modes and topological properties.

Findings

Zero and pi energy modes appear depending on symmetry and drive.

High frequency regime shows static-like topological features.

Frequency thresholds determine the existence of zero energy modes.

Abstract

We have investigated a periodically driven Creutz ladder in presence of two different driving protocols, namely, a sinusoidal drive and a $\delta$-kick imparted to the ladder at regular intervals of time. Specifically, we have studied the topological properties corresponding to the trivial and the non-trivial limits of the static (undriven) case via computing suitable topological invariants. Corresponding to the case where the chiral symmetry is intact, in addition to the zero energy modes, $\pi$ energy modes appear in both these cases. Further, two different frequency regimes of the driving protocol emerge, where Floquet-Magnus expansion is particularly employed to study the high frequency regime for the sinusoidal drive. Apart from the physics being identical in the high frequency and the static scenarios, the zero energy modes show distinctive features at low and high frequencies. For the sinusoidal drive, there exists a sharp frequency threshold beyond which the zero energy mode only exists in the topological limit, while in the trivial limit, it exists only upto the threshold frequency. In presence of the $\delta$-kick, the Creutz ladder demonstrates higher values of the topological invariant, and as a consequence the system possesses large number of edge modes.