Coupling between Charge, Lattice, Orbital, and Spin in a Charge Density Wave of 1$T$-TaS$_2$

摘要

Two-dimensional layered transition metal dichalcogenide (TMDC) materialsoften exhibit exotic quantum matter phases due to the delicate coupling andcompetitions between the charge, lattice, orbital, and spin degrees of freedom.Surprisingly, we here present, based on first-principles density-functionaltheory calculations, the incorporation of all such degrees of freedom in acharge density wave (CDW) of monolayer (ML) TMDC 1$T$-TaS$_2$. We reveal thatthe CDW formed via the electron-phonon coupling is significantly stabilized bythe orbital hybridization. The resulting lattice distortion to the "David-star"superstructure constituted of one cental, six nearest-neighbor, and sixnext-nearest-neighbor Ta atoms is accompanied by the formation ofquasimolecular orbitals due to a strong hybridization of the Ta $t_{\rm 2g}$orbitals. Furthermore, the flat band of the quasimolecular orbital at the Fermilevel has a spin splitting caused by an intramolecular exchange, yielding afull spin polarization with a band-gap opening. Our finding of the intricatecharge-lattice-orbital-spin coupling in ML 1$T$-TaS$_2$ provides a frameworkfor the exploration of various CDW phases observed in few-layer or bulk1$T$-TaS$_2$.