Unveiling the anharmonic reign: a unified framework for charge density wave transitions in monolayer H-MX₂ (M=Nb,Ta; X=S,Se)

The disparate charge density wave (CDW) behaviors in isostructural monolayer two-dimensional transition metal dichalcogenides (TMDs) pose a fundamental challenge to a unified understanding. Through ab initio anharmonic phonon analysis of monolayer H-MX₂ (M=Nb,Ta; X=S,Se), we establish a threefold regulatory principle: (1) Full suppression of CDW in H-NbS₂ via anharmonic effects, reversible under <0.6% biaxial strain; (2) Quantitative prediction of CDW transition temperatures (TCDW) spanning 65-112 K across compounds; (3) Identification of three microscopic drivers-dynamic charge transfer renormalization, q-dependent electron-phonon coupling strength, and correlation-influenced lattice instabilities. Our work establishes a unified, multiscale framework that not only resolves long-standing discrepancies in TMD phase diagrams but also provides clear design principles for predicting and strain-engineering CDW states in low-dimensional correlated materials.