From Symmetry to Stability: Structural and Electronic Transformation in Cs$_2$KInI$_6$

Cs$_2$KInI$_6$ is a promising lead-free halide double perovskite with a calculated direct band gap of 1.94 eV, ideal for solar cell applications. Our first-principles calculations reveal that its cubic phase (Fm$\bar{3}$m) is dynamically unstable. Using an accelerated machine learning approach, we identify 42 dynamically stable structures and further validate these findings using first-principles calculations on 11 of these. The most stable phase has Cmc$2_1$ symmetry with 20 atoms/unit cell. It lies 13 meV/atom above the convex hull but lacks octahedral cation coordination. The most stable perovskite-like structure has P$\bar{3}$ symmetry with 10 atoms/unit cell and low octahedral connectivity. Structure-property trade-offs are highlighted, with calculated distortions generally widening the band gap, shifting it from direct to indirect, and flattening the band edges. This work showcases the synergy of genetic algorithms, machine-learned potentials, and first-principles validation for discovering stable, complex materials.