Role of Ultrafast Electron-Thermal-Phonon Interactions in High Harmonic Generation and Dephasing from Graphene.

High harmonic generation (HHG) in solids arises when intense lasers drive attosecond-to-femtosecond electron dynamics within solid bands, causing high-energy emission. The main physical players in HHG are the electrons and photons, which are commonly thought to dictate HHG spectra. However, solids also host ubiquitous phonons that are usually relevant on longer timescales, and have therefore largely been neglected. It remains unclear if/how phonons partake in HHG and in dephasing of the electron dynamics, which has been very recently proposed. We theoretically study HHG in graphene by including optical phonons in the static limit, where the lattice is frozen on the electronic timescale and HHG is computed by sampling thermally occupied phonons and ensemble-averaging. We show that in graphene: (i) Optical-phonons strongly suppress HHG by coupling to interband currents and causing harmonic phase scrambling (destructive interference). This could potentially explain lack of experimental observation of HHG above ∼3 eV from graphene. (ii) HHG yields become temperature-dependent, though in graphene this dependence is weak due to phonon modes being frozen-out. (iii) Thermal phonons dephase interband coherences in a rate equivalent to