Based on first-principles
calculations, we propose a novel two-dimensional
(2D) germanium carbide, tetrahex-GeC
2
, and determine its
electronic and optical properties. Each Ge atom binds to four C atoms,
in contrast to the known 2D hexagonal germanium carbides. Monolayer
tetrahex-GeC
2
possesses a narrow direct band gap of 0.89
eV, which can be effectively tuned by applying strain and increasing
the thickness. Its electron mobility is extraordinarily high (9.5
× 10
4
cm
2
/(V s)), about 80 times that of
monolayer black phosphorus. The optical absorption coefficient is
∼10
6
cm
–1
in a wide spectral range
from near-infrared to near-ultraviolet, comparable to perovskite solar
cell materials. We obtain high cohesive energy (5.50 eV/atom), excellent
stability, and small electron/hole effective mass (0.19/0.10
m
0
). Tetrahex-GeC
2
turns out to be
a very promising semiconductor for nanoelectronic, optoelectronic,
and photovoltaic applications.