Charge density wave and spin 1/2 insulating state in single layer 1T-NbS2

In bulk samples and few layer flakes, the transition metal dichalcogenides NbS2 and NbSe2 assume the H polytype structure with trigonal prismatic coordination of the Nb atom. Recently, however, single and few layers of 1T-NbSe2 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-NbS2. We find that single-layer 1T-NbS2 undergoes a root 13 x root 13 star-of-David charge density wave. Within the generalized gradient approximation, the weak interaction between the stars leads to an ultraflat band that results to be located at the Fermi level and isolated from all other bands. The spin-polarized generalized gradient approximation stabilizes a total spin 1/2 magnetic state with a 0.21 mu(B) magnetic moment localized on the central Nb in the star and the opening of a 0.15 eV band gap. In the GGA + U framework, 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-NbSe2. 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.