  Using an evolutionary algorithm in combination with first-principles density
functional theory calculations, we identify two-dimensional (2D) CaP$_3$
monolayer as a new Dirac semimetal due to inversion and nonsymmorphic spatial
symmetries of the structure. This new topological material, composed of light
elements, exhibits high structural stability (higher than the phase known in
the literature), which is confirmed by thermodynamic and kinetic stability
analysis. Moreover, it satisfies the electron filling criteria, so that its
Dirac state is located near the Fermi level. The existence of the Dirac state
predicted by the theoretical symmetry analysis is also confirmed by
first-principles electronic band structure calculations. We find that the
energy position of the Dirac state can be tuned by strain, while the Dirac
state is unstable against an external electric field since it breaks the
spatial inversion symmetry. Our findings should be instrumental in the
development of 2D Dirac fermions based on light elements for their application
in nanoelectronic devices and topological electronics.
