Quantum spin Hall effect in rutile-based oxide multilayers

Dirac points in two-dimensional electronic structures are a source for topological electronic states due to the $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}$ Berry phase that they sustain. Here we show that two rutile multilayers [namely ${({\mathrm{WO}}₂)}₂/{({\mathrm{ZrO}}₂)}_n$ and ${({\mathrm{PtO}}₂)}₂/{({\mathrm{ZrO}}₂)}_n$], where an active bilayer is sandwiched by a thick enough ($n=6$ is sufficient) band insulating substrate, show semimetallic Dirac dispersions with a total of four Dirac cones along the $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}M$ direction. These become gapped upon the introduction of spin-orbit coupling, giving rise to an insulating ground state comprising four edge states. We discuss the origin of the lack of topological protection in terms of the valley spin-Chern numbers and the multiplicity of Dirac points. We show with a model Hamiltonian that mirror-symmetry breaking would be capable of creating a quantum phase transition to a strong topological insulator, with a single Kramers pair per edge.