Interacting weak topological insulators and their transition to Dirac semimetal phases*

Topological insulators in the presence of strong Coulomb interaction constitute novel phases of matter. Transitions between these phases can be driven by single-particle or many-body effects. On the basis of {\it ab-initio} calculations, we identify a concrete material, {\it i.e.} Ca$_{2}$PtO$_{4}$, that turns out to be a hole-doped weak topological insulator. Interestingly, the Pt-$d$ orbitals in this material are relevant for the band inversion that gives rise to the topological phase. Therefore, Coulomb interaction should be of importance in Ca$_{2}$PtO$_{4}$. To study the influence of interactions on the weak topological insulating phase, we look at a toy model corresponding to a layer-stacked 3D version of the Bernevig-Hughes-Zhang model with local interactions. For small to intermediate interaction strength, we discover novel interaction-driven topological phase transitions between the weak topological insulator and two Dirac semimetal phases. The latter correspond to gapless topological phases. For strong interactions, the system eventually becomes a Mott insulator.