Phonon Driven Floquet Matter.

The effect of electron-phonon coupling in materials can be interpreted as a dressing of the electronic structure by the lattice vibration, leading to vibrational replicas and hybridization of electronic states. In solids, a resonantly excited coherent phonon leads to a periodic oscillation of the atomic lattice in a crystal structure bringing the material into a nonequilibrium electronic configuration. Periodically oscillating quantum systems can be understood in terms of Floquet theory, which has a long tradition in the study of semiclassical light-matter interaction. Here, we show that the concepts of Floquet analysis can be applied to coherent lattice vibrations. This coupling leads to phonon-dressed quasi-particles imprinting specific signatures in the spectrum of the electronic structure. Such dressed electronic states can be detected by time- and angular-resolved photoelectron spectroscopy (ARPES) manifesting as sidebands to the equilibrium band structure. Taking graphene as a paradigmatic material with strong electron-phonon interaction and nontrivial topology, we show how the phonon-dressed states display an intricate sideband structure revealing the electron-phonon coupling at the Brillouin zone center and topological ordering of the Dirac bands. We demonstrate that if time-reversal symmetry is broken by the coherent lattice perturbations a topological phase transition can be induced. This work establishes that the recently demonstrated concept of light-induced nonequilibrium Floquet phases can also be applied when using coherent phonon modes for the dynamical control of material properties.