First-principles study of the electronic and optical properties of Ho $$_{\text{W}}$$ W impurities in single-layer tungsten disulfide

Abstract

Abstract The electronic and optical properties of single-layer (SL) tungsten disulfide (WS $$_2$$ 2 ) in the presence of substitutional Holmium impurities (Ho $$_{\text{W}}$$ W ) are studied. Although Ho is much larger than W, density functional theory (DFT) including spin-orbit coupling is used to show that Ho:SL WS $$_2$$ 2 is stable. The magnetic moment of the Ho impurity is found to be 4.75 $$\mu _B$$ μ B using spin-dependent DFT. The optical selection rules identified in the optical spectrum match exactly the optical selection rules derived by means of group theory. The presence of neutral Ho $$_W$$ W impurities gives rise to localized impurity states (LIS) with f-orbital character in the band structure. Using the Kubo-Greenwood formula and Kohn-Sham orbitals we obtain atom-like sharp transitions in the in-plane and out-of-plane components of the susceptibility tensor, Im $$\chi _{\parallel }$$ χ ‖ and Im $$\chi _{\perp }$$ χ ⊥ . The optical resonances are in good agreement with experimental data.