Quantum spin Hall phase in Mo₂M₂C₃O₂ (M = Ti, Zr, Hf) MXenes

The quantum spin Hall (QSH) phase is a peculiar physical phenomenon characterized by topologically protected helical edge states, with potential applications in lower-power electronics and spintronics. Here, using first-principles calculations, we predict the QSH phase in Mo₂M₂C₃O₂ (M = Ti, Zr, or Hf), new members with ordered structures in the family of two-dimensional transition metal carbides (MXenes). The QSH phase which is confirmed by the nontrivial Z₂ topological invariant and Dirac edge states arises from a d-d band inversion between the M-d_xy,x²−y² and the Mo-d_z² orbitals and a spin-orbital coupling (SOC)-induced splitting of the M-d_xy,x²−y² orbital at the Γ point. With different M atoms, the QSH gap of Mo₂M₂C₃O₂ ranges from 38 to 152 meV. These findings will broaden the scientific and technological impacts of both QSH materials and MXenes.