Electronic and optical properties of lanthanide-doped MoS 2 : Impact of ionic size and orbital configuration mismatch

Single-photon emitters (SPEs) are crucial for quantum technologies such as quantum simulation, secure quantum communication, and precision measurements. Two-dimensional transition-metal dichalcogenides (TMDCs) are promising SPE candidates because of their atomically thin nature and efficient photon extraction. However, their emission wavelengths limit compatibility with existing telecommunication technologies. Lanthanide doping in TMDCs, such as ${\mathrm{MoS}}₂$, offers a potential solution by introducing sharp, $f$-orbital derived emissions in the infrared range. Yet the feasibility of introducing these dopants remains uncertain due to the large ionic radii of the lanthanides. We employ density functional theory calculations to investigate the structural and electronic properties of lanthanide-doped ${\mathrm{MoS}}₂$ monolayers (Ln=Ce, Er). By evaluating formation energies with up to three adjacent S vacancies, we assess how these vacancies mitigate lattice strain caused by the size mismatch of Ce and Er with Mo. Our results show that while ${\mathrm{Ln}}_{\mathrm{Mo}}$ destabilizes the pristine lattice, S vacancies enhance thermodynamic stability. Charge-state analysis indicates that the defect states introduced by ${\mathrm{Ln}}_{\mathrm{Mo}}$ localize near the valence band and remain stable across a wide Fermi energy range. Electronic structure analysis shows that ${\mathrm{Ce}}⁴⁺$ and ${\mathrm{Er}}³⁺$ maintain their oxidation states upon electron doping due to additional acceptor states from host-induced dangling bonds. These states arise from an orbital filling mismatch between dopants and Mo. Furthermore, optical absorption analysis reveals multiple defect- and $f$-orbital-related transitions within the band gap range of the host material. In particular, ${\mathrm{Er}}_{\mathrm{Mo}}$ exhibits a weak $f\text{\ensuremath{-}}f$ absorption feature near 0.9--1.1 eV, consistent with known $4f$ transitions, while ${\mathrm{Ce}}_{\mathrm{Mo}}$ shows only defect-related absorption due to its empty $f$ shell.