Predicting alloy disorder effects on the Effective Band Structures (EBS) of Topological and other solid solutions.

Often interesting physics is found in system with a controlled loss of translational symmetry, most notably in substitutionally disordered alloys, defected crystals, quantum wells, or magnetically disordered spins, or finite nanostructures. Such absence of long-range order prevents in principle plotting and interpreting band structures in the primitive Brillouin zone (BZ), thereby losing a central tool in interpreting electronic structure. Instead, the community has been using large supercells—an efficient tool to include deviations from translational symmetry, yet producing, for energy levels, a complex spaghetti of bands that is difficult to communicate or interpret with the familiar tools of electronic structure theory of crystals. We use the Effective Band Structure (EBS) method [1,2] to map the spectral functions of supercells into primitive BZ, thus restoring the interpretive tools we are all familiar with. In this report, we show how DFT–based EBS helps us understand the tolerances of topological effects to different levels of disorder in HgTe-CdTe and PbSe-SnSe alloys.
(1) L.-W. Wang and A. Zunger, Phys. Rev. Lett. 80, 4725 (1998);
(2) V. Popescu, and A. Zunger, Phys. Rev. Lett. 104, 236403 (2010).