Figure 1

(a) Schematic shows a Ho\(_{\text{W}}\) impurity inside a \(8\times 8\times 1\) supercell of SL WS\(_2\). The grey circle depicts a Ho atom. The black (yellow) circles represent W (S) atoms. (b) The band structure and density of states (DOS) \(\rho (E)\) of pristine SL WS\(_2\) exhibits an in-plane band gap of \(E_{\parallel }=1.6\) eV and an out-of-plane band gap of \(E_{\perp }=3.2\) eV. States at the valence band edge are splitted due to SOC with \(\Delta _{SOC}=433\) meV. Gray region in the DOS plot specify the total DOS, while red blue and black curves are for d-orbitals of W, p-orbitals of S and the sum of the contributions, respectively. (c) Optical response of the pristine WS\(_{2}\), showing the in-plane and out-of-plane band gaps.