Time-reversal invariant realization of the Weyl semimetal phase

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.