Crystalline topological Dirac semimetal phase in rutile structure β′−PtO2

Based on first-principles calculations and symmetry analysis, we propose that a transition-metal rutile oxide, in particular ${\ensuremath{\beta}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{PtO}}_{2}$, can host a three-dimensional topological Dirac semimetal phase. We find that ${\ensuremath{\beta}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{PtO}}_{2}$ possesses an inner nodal chain structure when spin-orbit coupling is neglected. Incorporating spin-orbit coupling gaps the nodal chain while preserving a single pair of three-dimensional Dirac points protected by a screw rotation symmetry. These Dirac points are created by a band inversion of two $d$ bands, which is a realization of a Dirac semimetal phase in a correlated electron system. Moreover, a mirror plane in the momentum space carries a nontrivial mirror Chern number ${n}_{M}=\ensuremath{-}2$, which distinguishes ${\ensuremath{\beta}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{PtO}}_{2}$ from the Dirac semimetals known so far, such as ${\mathrm{Na}}_{3}\mathrm{Bi}$ and ${\mathrm{Cd}}_{3}{\mathrm{As}}_{2}$. If we apply a perturbation that breaks the rotation symmetry and preserves the mirror symmetry, the Dirac points are gapped, and the system becomes a topological crystalline insulator.