Restoring E vs k band structure dispersion in low symmetry disordered systems

Many target properties of materials are not readily available for pure components AX or BX but do exist in alloys of (AX)_x(BX)_1-x. Substitutional alloy disorder generally results in the distribution of local environments as well as symmetry-breaking atomic displacements as seen in EXAFS, leading to the removal of band degeneracies and meaning of sharp wavevectors k hence E vs k band dispersion. These effects are not treatable by single-site disorder theories such as CPA. Supercells do retain atomic resolution of disorder but do not readily produce E vs k dispersion needed to judge topological properties. We combine supercells with band unfolding [1] in alloys, leading to Effective Band Structure which recognizes local symmetry yet informs about the extent to which the long-range translational symmetry is retained. We show how the scale of disorders in alloy systems, such as PbS-PbTe, PbSe-SnSe, CdTe-HgTe, PM phase Mott insulators and ABO3 perovskites affects the topological properties, and how the restored band dispersion helps us to understand experimental observations.
1. V. Popescu and A. Zunger, Phys. Rev. Lett. 104, 236403 (2010).