  We report the electronic, the thermal, and the optical properties of a
Germagraphene (GeC) monolayer taking into account buckling effects. The
relatively wide direct band gap of a flat GeC nanosheet can be changed by
tuning the planar buckling. A GeC monolayer has an sp$^2$ hybridization in
which the contribution of an $s$-orbital is half of the contribution of a
$p$-orbital leading to stronger $\sigma\text{-}\sigma$ bonds compared to the
$\sigma\text{-}\pi$ bonds. Increasing the planar buckling, the contribution of
an $s$-orbital is decreased while the contribution of a $p$-orbital is
increased resulting in a sp$^3$-hybridization in which the $\sigma\text{-}\pi$
bond becomes stronger than the $\sigma\text{-}\sigma$ bond. As a result, the
band gap of a buckled GeC is reduced and thus the thermal and the optical
properties are significantly modified. We find that the heat capacity of the
buckled GeC is decreased at low values of planar buckling, which is caused by
the anticrossing of the optical and the acoustic phonon modes affecting phonon
scattering processes. The resulting optical properties, such as the dielectric
function, the refractive index, the electron energy loss spectra, the
absorption, and the optical conductivity show that a buckled GeC nanosheet has
increased optical activities in the visible light region compared to a flat
GeC. The optical conductivity is red shifted from the near ultraviolet to the
visible light region, when the planar buckling is increased. We can thus
confirm that the buckling can be seen as another parameter to improve GeC
monolayers for optoelectronic devices.
