Re-entrant Quantum Spin Hall State in Charge-Density Wave Phase of Doped Single-Layer Transition Metal Dichalcogenides

We explore doping induced phase transitions in single-layer 1T'-TMDs, MTe₂ (M = Mo and W), based on first-principles calculations. As increasing electron doping, we find that several new collective phases with nontrivial topological properties stabilize. At a low doping region, we obtain a dome-shaped conventional superconducting phase and the transition temperature reaches around 9 K. At an intermediate doping region, we find a 2 x 5 charge-density wave (CDW) phase with nontrivial topological properties. Such a peculiar lattice distortion retains a nonsymmorphic symmetry with/without inversion symmetry that gives rise to symmetry-protected Dirac/Weyl points. At a high doping region, we find a 2 x 2 CDW with the diamond shape chain structure with rather larger energy gap. The 2 x 2 CDW phase also supports the symmetry protected Weyl points. We anticipate that present results will pave the way for the research on the correlated phenomena and nontrivial topological aspect in TMDs by controlled manner.