Floquet edge states in a harmonically driven integer quantum Hall system

TL;DR

This paper investigates the emergence and robustness of counter-propagating Floquet edge states in a harmonically driven quantum Hall system, revealing their generic presence and stability against static disorder through phase diagram analysis and spectral examination.

Contribution

It demonstrates that counter-propagating Floquet edge modes are a generic feature of periodically driven quantum Hall systems and analyzes their spectral properties and robustness.

Findings

Counter-propagating Floquet edge modes appear in driven quantum Hall systems.

These modes are robust against static perturbations that preserve chiral edge states.

The phase diagram shows topologically distinct phases with such edge modes.

Abstract

Recent theoretical work on time-periodically kicked Hofstadter model found robust counter-propagating edge modes. It remains unclear how ubiquitously such anomalous modes can appear, and what dictates their robustness against disorder. Here we shed further light on the nature of these modes by analyzing a simple type of periodic driving where the hopping along one spatial direction is modulated sinusoidally with time while the hopping along the other spatial direction is kept constant. We obtain the phase diagram for the quasienergy spectrum at flux 1/3 as the driving frequency $\omega$ and the hopping anisotropy are varied. A series of topologically distinct phases with counter-propagating edge modes appear due to the harmonic driving, similar to the case of a periodically kicked system studied earlier. We analyze the time dependence of the pair of Floquet edge states localized at the same edge, and compare their Fourier components in the frequency domain. In the limit of small modulation, one of the Floquet edge mode within the pair can be viewed as the edge mode originally living in the other energy gap shifted in quasienergy by $\hbar \omega$, i.e., by absorption or emission of a "photon" of frequency $\omega$. Our result suggests that counter-propagating Floquet edge modes are generic features of periodically driven integer quantum Hall systems, and not tied to any particular driving protocol. It also suggests that the Floquet edge modes would remain robust to any static perturbations that do not destroy the chiral edge modes of static quantum Hall states.