# Charge density wave and spin $1/2$ insulating state in single layer 1T-NbS$_2$

## TL;DR

This study uses first-principles calculations to reveal that single-layer 1T-NbS2 exhibits a charge density wave and a spin-1/2 magnetic insulating state, with potential for synthesis similar to 1T-NbSe2.

## Contribution

It demonstrates the existence of a charge density wave and magnetic insulating state in single-layer 1T-NbS2, highlighting its structural stability and magnetic properties using advanced computational methods.

## Key findings

- 1T-NbS2 has a $\sqrt{13} imes\sqrt{13}$ charge density wave.
- The material exhibits a spin-1/2 magnetic state with a 0.15 eV band gap.
- Exchange interactions suggest ferromagnetic coupling between stars.

## Abstract

In bulk samples and few layer flakes, the transition metal dichalcogenides NbS$_2$ and NbSe$_2$ assume the H polytype structure with trigonal prismatic coordination of the Nb atom. Recently, however, single and few layers of 1T-NbSe$_2$ with octahedral coordination around the transition metal ion were synthesized. Motivated by these experiments and by using first-principles calculations, we investigate the structural, electronic and dynamical properties of single layer 1T-NbS$_2$. We find that single-layer 1T-NbS$_2$ undergoes a $\sqrt{13}\times\sqrt{13}$ star-of-David charge density wave. Within the generalized gradient approximation, the weak interaction between the stars leads to an ultraflat band at the Fermi level isolated from all other bands. The spin-polarized generalized gradient approximation stabilizes a total spin $1/2$ magnetic state with opening of a $0.15$ eV band gap and a $0.21\mu_B$ magnetic moment localized on the central Nb in the star. Within GGA+U, the magnetic moment on the central Nb is enhanced to $0.41\mu_{B}$ and a larger gap occurs. Most important, this approximation gives a small energy difference between the 1T and 1H polytypes (only $+0.5$ mRy/Nb), suggesting that the 1T-polytype can be synthesized in a similar way as done for single layer 1T-NbSe$_2$. Finally we compute first and second nearest neighbors magnetic inter-star exchange interactions finding $J_1$=9.5~K and $J_2$=0.4~K ferromagnetic coupling constants.