We report on the effect of laser illumination with circularly polarized light on the electronic structure of $AB$-stacked graphite samples. By using Floquet theory in combination with Green's function techniques, we find that the polarized light induces band-gap openings at the Floquet zone edge $\hslash \mathrm{\Omega }/2$, bridged by chiral boundary states. These states propagate mainly along the borders of the constituting layers as evidenced by the time-averaged local density of states and the probability current density in several geometries. Semianalytic calculations of the Chern number suggest that these states are of topological nature, similar to those found in illuminated 2D samples like monolayer and bilayer graphene. These states are promising candidates for the realization of a three-dimensional version of the quantum Hall effect for Floquet systems.

• Received 5 November 2019
• Revised 17 January 2020
• Accepted 31 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.075424