Entangled States Induced by Electron-Phonon Interaction in Two-Dimensional Materials

We report on the effects of electron-phonon interaction in materials such as graphene, showing that it enables the formation of a gap bridged by unique edge states. These states exhibit a distinctive locking among propagation direction, valley, and phonon mode, allowing for the generation of electron-phonon entangled states whose parts can be easily split. We discuss the effect of the chiral atomic motion in the zone boundary phonons leading to this effect. Our findings shed light on how to harness these unconventional states in quantum research.