LAUSR

Two-dimensional layered transition-metal-dichalcogenide (TMDC) materials often exhibit exotic quantum phases due to the delicate coupling and competitions of charge, lattice, orbital, and spin degrees of freedom. Surprisingly, we here present, based on first-principles density-functional theory calculations, the incorporation of all such degrees of freedom in a charge density wave (CDW) of monolayer (ML) TMDC $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$. We reveal that this CDW accompanying the lattice distortion to the ``David-star'' (DS) superstructure constituted of one cental, six nearest-neighbor, and six next-nearest-neighbor Ta atoms is driven by the formation of quasimolecular orbitals due to a strong hybridization of Ta ${t}_{2\mathrm{g}}$ orbitals. The resulting weakly overlapped nonbonding orbitals between the DS clusters form a narrow half-filled band at the middle of the CDW gap, leading to the Stoner-type magnetic instability caused by an intramolecular exchange interaction. It is thus demonstrated that the Stoner parameter $I$ corresponding to the effective on-site Coulomb interaction $U$ opens a Mott gap. Our finding of the intricate charge-lattice-orbital-spin coupling in ML $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ provides a framework for the exploration of various CDW phases observed in few-layer or bulk $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$.