Topological insulators in the ordered double transition metals M2′MC2 MXenes (M′ = Mo, W; M = Ti, Zr, Hf)

The family of two-dimensional transition metal carbides, so called MXenes, has recently found new members with ordered double transition metals M-2'M '' C-2, where M' and M '' stand for transition metals. Here, using a set of first-principles calculations, we demonstrate that some of the newly added members, oxide M-2'M '' C-2 (M', = Mo, W; M '' = Ti, Zr, Hf) MXenes, are topological insulators. The nontrivial topological states of the predicted MXenes are revealed by the Z(2) index, which is evaluated from the parities of the occupied bands below the Fermi energy at time reversal invariant momenta, and also by the presence of the edge states. The predicted M-2'M '' C2O2 MXenes show nontrivial gaps in the range of 0.041-0.285 eV within the generalized gradient approximation and 0.119-0.409 eV within the hybrid functional. The band gaps are induced by the spin-orbit coupling within the degenerate states with d(x2 -y2) and d(xy) characters of M' and M '', while the band inversion occurs at the Gamma point among the degenerate d(x2 -y2)/d(xy) orbitals and a nondegenerate d(3z2-r2) orbital, which is driven by the hybridization of the neighboring orbitals. The phonon dispersion calculations find that the predicted topological insulators are structurally stable. The predicted W-based MXenes with large band gaps might be suitable candidates for many topological applications at room temperature. In addition, we study the electronic structures of thicker ordered double transition metals M-2'M-2 '' C2O2 (M' = Mo, W; M '' = Ti, Zr, Hf) and find that they are nontrivial topological semimetals. Among the predicted topological insulators and topological semimetals, Mo2TiC2 and Mo2Ti2C3 functionalized with a mixture of F, O, and OH have already been synthesized, and therefore some of the topological materials proposed here can be experimentally accessed.