Scalable Mapping of Defects and Order–Disorder Transitions in In-Doped SnBi₂Te₄

The search for tunable superconductivity and topological transitions in layered chalcogenides motivates our investigation of In-doped SnBi₂Te₄, a nonmagnetic analog of MnBi₂Te₄ with debated topological character. Using first principles–trained cluster expansion model and performing finite-temperature Monte Carlo sampling (Metropolis algorithm), we mapped the composition–temperature phase behavior and defect statistics in Sn_1-x+y(In_x)Bi_2-yTe₄. The surrogate reproduces DFT energetics within ~1 meV/atom and captures disorder energetics across Sn/In/Bi sublattices. Simulations reveal composition-dependent defect clustering with distinct order–disorder transitions: a low-T regime driven by local site ordering and a higher-T regime associated with antisite activation on the Bi/Sn planes. The resulting trends provide practical processing windows that suppress harmful antisites while stabilizing desired In site occupancies. Together, these results demonstrate a predictive, robust pathway for defect-aware design in topological layered quantum materials.