When Defects Become the Crystal: Periodic Mirror-Twin Boundary Phases in Substoichiometric 2D-MoTe ₂

Defect concentrations in crystalline matter can be tuned by growth and postsynthesis processing conditions. Point defects may condense into extended defects, and their ordering into periodic arrays creates novel materials. We show that Mo-rich mirror-twin grain boundary (MTB) loops in MoTe₂ arrange into periodic phases under conditions that balance Te-chemical potential and thermal activation. These MTB phases give rise to a homologous series with various stoichiometries. While there are many possible arrangements of MTBs, our ab initio calculations show that the observed phases all lie on or very close to the convex hull. These thermodynamic equilibrium considerations provide a unified theory for the stability of the five MTB phases reported here. Density functional theory simulations indicate that these MTB phases exhibit Kagome-like flat bands with potential for exhibiting many-body phenomena and thus suggesting an approach for defect-engineering quantum properties in systems with reduced dimensionality.