Gate-tunable superconductivity and charge-density wave in monolayer 1T'-MoTe₂ and 1T'-WTe₂

Using first-principles calculation methods, we reveal a series of phase transitions as a function of gating or electron doping in monolayered quantum spin Hall (QSH) insulators, 1T'-MoTe₂ and 1T'-WTe₂. With increasing electron doping, we show that a phonon mediated superconducting phase is realized first and is followed by a charge density wave (CDW) phase with a nonsymmorphic lattice symmetry. The newly found CDW phase exhibits Weyl energy bands with spin-orbit coupling with fractional band filling, and reforms into a topological nontrivial phase with fully filled bands. The robust resurgence of the QSH state coexisting with the CDW phase is shown to originate from band inversions induced by the nonsymmorphic lattice distortion through the strong electron-phonon interaction, thus suggesting the realization of various interfacial states between superconducting states, and various CDW and topological states on a two-dimensional crystal by inhomogeneous gating or doping.