Ab initio study of $Z_2$ topological phases in perovskite (111) $({\text{SrTiO}}_3{)}_7\mathrm{/}({\text{SrIrO}}_3{)}_2$ and $({\text{KTaO}}_3{)}_7\mathrm{/}({\text{KPtO}}_3{)}_2$ multilayers

Honeycomb structures formed by the growth of perovskite 5d transition metal oxide heteroestructures along the (111) direction in $t_{2g}^5$ configuration can give rise to topological ground states characterized by a topological index $\nu$=1. Using a combination of a tight binding model and ab initio calculations we study the multilayers $({\text{SrTiO}}_3{)}_7\mathrm{/}({\text{SrIrO}}_3{)}_2$ and $({\text{KTaO}}_3{)}_7\mathrm{/}({\text{KPtO}}_3{)}_2$ as a function of parity asymmetry, on-site interaction and uniaxial strain and determine the nature and evolution of the gap. $({\text{SrTiO}}_3{)}_7\mathrm{/}({\text{SrIrO}}_3{)}_2$ is found to be a topological semimetal. $({\text{KTaO}}_3{)}_7\mathrm{/}({\text{KPtO}}_3{)}_2$ is a topological Mott insulator that can be driven to a trivial insulating phase by an external electric field.