First-principles calculations were performed to investigate the phase stability and transition within four monolayer transition-metal dichalcogenide (TMD) systems, i.e., MX2 (M = Mo or W and X = S or Se) under coupled electron doping and lattice deformation. With the lattice distortion and electron doping density treated as state variables, the energy surfaces of different phases were computed, and the diagrams of energetically preferred phases were constructed. These diagrams assess the competition between different phases and predict conditions of phase transitions for the TMDs considered. The interplay between lattice deformation and electron doping was identified as originating from the deformation induced band shifting and band bending. Based on our findings, a potential design strategy combining an efficient electrolytic gating and a lattice straining to achieve controllable phase engineering in TMD monolayers was demonstrated.

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