Quantum embedding studies of substitutional Er³⁺ defects in monolayer WS₂

Single rare-earth (RE) impurities feature electronically screened 4f states that result in hours-long coherence times and, in the case of Er³⁺, homogeneous linewidths as narrow as 50 Hz within the telecom band. Harnessing the intrinsic potential of Er³⁺ and other REs as spin-qubits requires finding suitable host materials that avoid unwanted decoherence sources, e.g., strain and hyperfine interactions, while being easily integrated with current device technology. An interesting option along these lines is tungsten disulfide (WS₂), a low spin-active-nuclei van der Waals material with a 2.1-eV bandgap and sizable lattice constant. Motivated by these considerations, we employ computational methods based on quantum embedding techniques to study an Er³⁺ substitution (Er_W) in monolayer WS₂. The technique has been applied to similar systems and is based on the constrained random phase approximation (cRPA) and a localized basis via Wannierization to construct an effective Hamiltonian that explicitly treats the correlations within a subspace chosen to comprise the 4f-like defect states of the Er_W center. Spin-orbit interactions are added both implicitly within the cRPA and explicitly within the effective Hamiltonian through atomic-like spin-orbit terms. The obtained results within these methods help in describing the electronic structure and 4f–4f excitations of Er³⁺ more quantitatively, with the potential for being extended to other defect systems based on RE dopants in similar host matrices.