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

We study theoretically AB-stacked honeycomb bilayers driven by light in resonance with an infrared phonon within a tight-binding description. We characterize the phonon properties of honeycomb bilayers with group theory and construct an electronic time-dependent tight-binding model for the system following photoexcitation in resonance with an infrared phonon. We adopt an atomically adiabatic approximation [V. Mohanty and E. J. Heller, Proc. Natl. Acad. Sci. 116, 18316 (2019)PNASA60027-842410.1073/pnas.1908624116] to describe classically vibrating nuclei, but obtain the Floquet quasienergy spectrum associated with the time-dependent model exactly. We introduce a general scheme to disentangle the complex low-frequency Floquet spectrum to elucidate the relevant Floquet bands. As a prototypical example, we consider bilayer graphene. We find that light in the low-frequency regime can induce a band gap in the quasienergy spectrum in the vicinity of the K points even if it is linearly polarized, in contrast with the expectations within the Born-Oppenheimer approximation and the high-frequency regime. Finally, we analyze the diabaticity of the driven electron and driven phonon processes and find contrasting effects on the autocorrelation functions at the same driving frequency: Driven phonons preserve the character of the initial state while driven electrons exhibit strong deviations within a few drive cycles. The procedure outlined here can be applied to other materials to describe the combined effects of low-frequency light on phonons and electrons.