  Due to its linear dispersion, monolayer graphene is expected to generate a
third harmonic response at terahertz frequencies. There have been a variety of
different models of this effect and recently it has been experimentally
observed. However, there is still considerable uncertainty as to the role of
scattering on harmonic generation in graphene. In this work, we model
third-harmonic generation in doped monolayer graphene at THz frequencies by
employing a nearest-neighbour tight-binding model in the length gauge. We
include optical phonon and neutral impurity scattering at the microscopic
level, and examine the effects of scattering on the third harmonic response. We
also compare the results of a phenomenological semiclassical theory, using a
field-dependent scattering time extracted from the simulation, and find a
significantly lower third harmonic field than that found from the microscopic
model. This demonstrates that third-harmonic generation is much more sensitive
to the nature of the scattering than is the linear response. We also compare
the results of our full simulation to recent experimental results and find
qualitative agreement.
