  We consider a natural generalization of the lattice model for a periodic
array of two layers, A and B, of spinless electrons proposed by Fu [Phys. Rev.
Lett. 106, 106802 (2011)] as a prototype for a crystalline insulator. This
model has time-reversal symmetry and broken inversion symmetry. We show that
when the intralayer next-nearest-neighbor hoppings ta2, a = A, B vanish, this
model supports a Weyl semimetal phase for a wide range of the remaining model
parameters. When the effect of ta2 is considered, topological crystalline
insulating phases take place within the Weyl semimetal one. By mapping to an
effective Weyl Hamiltonian we derive some analytical results for the phase
diagram as well as for the structure of the nodes in the spectrum of the Weyl
semimetal.
