# Floquet oscillations in periodically driven Dirac systems

## TL;DR

This paper demonstrates that periodically driven Dirac systems can exhibit Floquet oscillations, analogous to Bloch oscillations, with tunable periods and richer patterns, observable in materials like graphene under circularly polarized light.

## Contribution

It introduces the concept of Floquet oscillations in Dirac systems and shows how they can be generated and analyzed using different driving protocols.

## Key findings

- Floquet oscillations occur in driven Dirac systems with linear dispersion.
- Oscillation patterns are richer than traditional Bloch oscillations.
- Oscillation period can be tuned via driving frequency.

## Abstract

Electrons in a lattice exhibit time-periodic motion, known as Bloch oscillation, when subject to an additional static electric field. Here we show that a corresponding dynamics can occur upon replacing the spatially periodic potential by a time-periodic driving: Floquet oscillations of charge carriers in a spatially homogeneous system. The time lattice of the driving gives rise to Floquet bands that take on the role of the usual Bloch bands. For two different drivings (harmonic driving and periodic kicking through pulses) of systems with linear dispersion we demonstrate the existence of such oscillations, both by directly propagating wave packets and based on a complementary Floquet analysis. The Floquet oscillations feature richer oscillation patterns than their Bloch counterpart and enable the imaging of Floquet bands. Moreover, their period can be directly tuned through the driving frequency. Such oscillations should be experimentally observable in effective Dirac systems, such as graphene, when illuminated with circularly polarized light.