Dynamic stability of the single-layer transition metal dichalcogenides

In the quest for advanced semi-conductors, we have expanded our knowledge on a series of single-layer TMDs by calculating the electronic structure and lattice dynamic stability based on the first-principles density functional theory. The single layers of Mo and W dichalcogenides are found to be stable with P-6m2 symmetry. The reduction of dimension opens up and increases the bandgap. The charge transfer is found to decrease from sulfide to selenide and to telluride due to the decrease of electronegativity of chalcogen, which also induces the reduction of bandgap. The TA mode softening is found along Γ–K direction and becomes more significant from sulfide to selenide and to telluride in the single-layer TMDs of Mo and W, which corresponds to the vibration of transition metal cations along y-axis. The single layers of Nb dichalcogenides are found to be instable with P-6m2 symmetry but stable with P-3m1 symmetry. It is also speculated that the interactions of cations mediated by electron–phonon coupling are accountable for the dynamic instability of the single-layer TMDs of Nb with P-6m2 symmetry. The unstable P-6m2 single-layer Nb dichalcogenides can transform to the stable P-3m1 structure during the exfoliation from the bulk, via the displacement of two anion layers of the sandwich structure.