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Using first-principles calculation methods, we reveal a series of phasetransitions as a function of electron doping in single-layer 1T$'$-MoTe$_2$ and1T$'$-WTe$_2$ exhibiting quantum spin Hall (QSH) edge states without doping. Asincreasing doping, we show that a phonon mediated superconducting phase firstrealizes and is followed by a charge density wave (CDW) phase with anonsymmorphic lattice symmetry. The newly found CDW phase exhibits Dirac orWeyl energy bands with a spin-orbit coupling in case of a fractional bandfilling and re-enters into topological insulating phase with fully filledbands. The robust resurgence of QSH state coexisting with the CDW phase isshown to originate from band inversions induced by the nonsymmorphic latticedistortion through the strong electron-phonon interaction, thus suggesting arealization of various interfacial states between superconducting, density waveand topological states on a two-dimensional crystal only by doping.

Reentrant Quantum Spin Hall States in Charge Density Wave Phase of Doped Single-Layer Transition Metal Dichalcogenides