Since the early days of the quantum theory of solids, the interaction between electrons
and lattice vibrations has provided a long list of exciting discoveries. Examples include the role played by electron-phonon (e-ph) interaction in the development of the theory of
superconductivity and conducting polymers, where charge doping is used to circumvent the Peierls transition. In the last decade, the theoretical prediction and observation of phonons with intrinsic chirality in two-dimensional materials brought a new ingredient to this long standing problem. In this talk I will present our recent results on the effects of the interaction between electrons and phonons in two-dimensional materials [1,2,3]. By using a non-perturbative solution, we demonstrate that electron-phonon interactions trigger inelastic Umklapp processes, leading to peculiar 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 efft. Our findings shed light on harnessing these unconventional states in quantum research.

[1]J. Medina Dueñas, H. L. Calvo, L. E. F. Foa Torres, Phys. Rev. Lett. 128, 066801 (2022).
[2]J. Mella, H. L. Calvo, L. E. F. Foa Torres, Nano Letters 23, 11013 (2023).
[3] For related research see https://www.foatorres.com/