  We theoretically investigate high-harmonic generation (HHG) in
honeycomb-lattice graphene models when subjected to a DC electric field. By
integrating the quantum master equation with the Boltzmann equation, we develop
a numerical method to compute laser-driven dynamics in many-electron lattice
systems under DC electric current. The method enables us to treat both the
weak-laser (perturbative) and intense-laser (nonperturbative) regimes in a
unified way, accounting for the experimentally inevitable dissipation effects.
From it, we obtain the HHG spectra and analyze their dependence on laser
frequency, laser intensity, laser-field direction, and DC current strength. We
show that the dynamical and static symmetries are partially broken by a DC
current or staggered potential term, and such symmetry breakings drastically
change the shape of the HHG spectra, especially in terms of the presence or
absence of $(2n+1)$th-, $2n$th-, or $3n$th-order harmonics ($n\in \mathbb Z$).
The laser intensity, frequency, and polarization are also shown to affect the
shape of the HHG spectra. Our findings indicate that HHG spectra in conducting
electron systems can be quantitatively or qualitatively controlled by tuning
various external parameters, and DC electric current is used as such an
efficient parameter.
