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

TL;DR

This study uses first-principles calculations to reveal the complex coupling of charge, lattice, orbital, and spin degrees of freedom in a charge density wave of monolayer 1T-TaS2, highlighting the stabilization mechanisms and resulting electronic structure.

Contribution

It demonstrates the incorporation of all degrees of freedom in modeling the CDW in monolayer 1T-TaS2, revealing the role of orbital hybridization and spin polarization in stabilizing the phase.

Findings

Charge density wave stabilized by orbital hybridization.

Formation of quasimolecular orbitals with spin splitting.

Full spin polarization and band-gap opening at Fermi level.

Abstract

Two-dimensional layered transition metal dichalcogenide (TMDC) materials often exhibit exotic quantum matter phases due to the delicate coupling and competitions between the 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 1$T$-TaS$_2$. We reveal that the CDW formed via the electron-phonon coupling is significantly stabilized by the orbital hybridization. The resulting lattice distortion to the "David-star" superstructure constituted of one cental, six nearest-neighbor, and six next-nearest-neighbor Ta atoms is accompanied by the formation of quasimolecular orbitals due to a strong hybridization of the Ta $t_{\rm 2g}$ orbitals. Furthermore, the flat band of the quasimolecular orbital at the Fermi level has a spin splitting caused by an intramolecular exchange, yielding a full spin polarization with a band-gap opening. Our finding of the intricate charge-lattice-orbital-spin coupling in ML 1$T$-TaS$_2$ provides a framework for the exploration of various CDW phases observed in few-layer or bulk 1$T$-TaS$_2$.