First-principles study of dual-site Sr–M (M = Ga, Hf, Ge) co-doping in the perovskite solid electrolyte Li_0.5La_0.5TiO₃: effects on Li⁺ migration and electronic insulation

The perovskite Li_0.5La_0.5TiO₃ (LLTO) is an attractive solid electrolyte for all-solid-state battery applications because of its favorable Li⁺ transport characteristics. Its properties could be further improved through doping with selected elements, which can modify its ionic conductivity and structural stability. In this work, first-principles density functional theory calculations were carried out to systematically investigate the influence of dual-site substitution in tetragonal LLTO on its stability, electronic insulation, and Li-ion transport properties, based on the general formula La_1−xSr_xLiTi_2−yM_yO₆ (M = Ga, Hf, or Ge). The pristine LLTO crystallizes in the tetragonal P4/mmm structure and is energetically favorable, as evidenced by its negative formation energy, and exhibits an indirect band gap of 1.82 eV. Upon co-doping, the band gap increases to 2.12 eV for Sr–Ga, 2.24 eV for Sr–Hf, and 2.15 eV for Sr–Ge, indicating improved electronic insulation without the formation of mid-gap defect states. Migration barrier analysis using the climbing-image nudged elastic band method shows a significant reduction to 0.39–0.49 eV for Sr–Ga co-doping, while Sr–Ge provides moderate improvement and Sr–Hf increases the barriers. The enhanced Li-ion transport in Sr–Ga-doped LLTO is attributed to an optimized Li–O bottleneck geometry and a smoother diffusion landscape. These results demonstrate that rational A- and B-site engineering could be an effective strategy for tuning ionic transport while preserving the structural integrity of the perovskite solid electrolyte LLTO.