  DC photoelectrical currents can be generated purely as a non-linear effect in
uniform media lacking inversion symmetry without the need for a material
junction or bias voltages to drive it, in what is termed photogalvanic effect.
These currents are strongly dependent on the polarization state of the
radiation, as well as on topological properties of the underlying Fermi surface
such as its Berry curvature. In order to study the intrinsic photogalvanic
response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal
boron nitride (hBN), we compute the non-linear current using a perturbative
expansion of the density matrix. This allows a microscopic description of the
quadratic response to an electromagnetic field in these materials, which we
analyze as a function of temperature and electron density. We find that the
intrinsic response is robust across these systems and allows for currents in
the range of pA cm/W to nA cm/W. At the independent-particle level, the
response of hBN-based structures is significant only in the ultra-violet due to
their sizeable band-gap. However, when Coulomb interactions are accounted for
by explicit solution of the Bethe-Salpeter equation, we find that the
photoconductivity is strongly modified by transitions involving exciton levels
in the gap region, whose spectral weight dominates in the overall frequency
range. Biased bilayers and gapped monolayers of graphene have a strong
photoconductivity in the visible and infrared window, allowing for photocurrent
densities of several nA cm/W. We further show that the richer electronic
dispersion of BBG at low energies and the ability to change its band-gap on
demand allows a higher tunability of the photocurrent, including not only its
magnitude but also, and significantly, its polarity.
