Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light.

We theoretically study AB-stacked honeycomb bilayers driven by infrared light and consider the electronic and phononic degrees of freedom on equal footing within a tight-binding description. First, we characterize the phonon properties of an AB-stacked honeycomb bilayer with group theory, with the $D_{3d}$ point group. We construct a tight-binding model that captures the effects of the lattice distortions induced by the activation of in-plane infrared modes by light. We discuss the phonons' dynamical response following photo-excitation and their subsequent effect on the electronic band structure within low-frequency Floquet perturbation theory. As a prototypical example, we consider bilayer graphene. We find that the coupling of light with the phonons induces topological band transitions within the adiabatic approximation, in analogy with the effects of strain. The topological band transition is not present when only considering the coupling of the infrared laser with the electrons. To lowest-order in Floquet perturbation theory, the linearly polarized light in the low-frequency regime can induce a bandgap in the quasienergy spectrum in the vicinity of the $K$ points. Numerical solutions of the Floquet-Schrodinger equation confirms this effect. The procedure outlined here can be applied to other van der Waal materials to describe the combined effects of low-frequency light on phonons and electrons.