Unveiling hidden charge density waves in single-layer NbSe2 by impurities

We employ ab initio calculations to investigate the charge density waves in single-layer NbSe2, and we explore how they are affected by transition metal atoms. Our calculations reproduce the observed orthorhombic phase in single-layer NbSe2 in the clean limit, establishing the energy order between three different distorted structures, two consisting of triangular Nb-Nb clusters and a third, energetically unfavored, consisting of hexagonal Nb-Nb clusters. Such energy order, in agreement with known experimental work, is reversed by the adsorption of Co and Mn, which favor the formation of hexagonal Nb-Nb clusters; this CDW structure is indeed allowed from a symmetry point of view but hidden in pure single layers because it is at a higher energy. The other adsorbates, K and Ga, still favor one of the triangular Nb-Nb cluster, while suppressing the other. We report how the energy difference between such distorted structure varies with these adsorbates. Furthermore, transition metals induce magnetism and favor the reduction of the symmetry of the charge density distribution.