  We propose a realization of the Weyl semimetal phase that is invariant under
time reversal and occurs due to broken inversion symmetry. We consider both a
simple superlattice model and a more realistic tight-binding model describing
an experimentally reasonable HgTe/CdTe multilayer structure. The two models
have the same underlying symmetry, therefore their low-energy features are
equivalent. We find a Weyl semimetal phase between the normal insulator and the
topological insulator phases that exists for a finite range of the system
parameters and exhibits a finite number of Weyl points with robust band
touching at the Fermi level. This phase is experimentally characterized by a
strong conductivity anisotropy and topological surface states. The principal
conductivities change in a complementary fashion as the system parameters are
varied, and the surface states only exist in a region of momentum space that is
determined by the positions of the Weyl points.
