Alloy theory with atomic resolution for Rashba or topological systems

Interest in substitutional disordered alloys has recently reemerged with focus on the symmetry-sensitive properties in the alloy such as topological insulation and Rashba effect. A substitutional random alloy manifests a distribution of local environments, creating a polymorphous network. While the macroscopic average (monomorphous) structure may have the original high symmetry of the constituent compounds, many observable physical properties are sensitive to local symmetry, and are hence $<P(S_i)>$ rather than $P(S_0)$=$P(<S_i>)$. The fundamental difference between polymorphous $<P(S_i)>$ and monomorphous $P(S_0)$ led to the often-diverging results and the missing the atomic-scale resolution needed to discern symmetry-related physics. A natural approach capturing the polymorphous aspect is supercell model, which however suffers the difficulty of band folding ('spaghetti bands'), rendering the E vs k dispersion needed in topology and Rashba physics and seen in experiments, practically inaccessible. A solution that retains the polymorphous nature but restores the E vs k relation is to unfold the supercell bands. This yields alloy Effective Band Structure (EBS), providing a 3D picture of spectral density consisting of E- and k-dependent spectral weight with coherent and incoherent features, all created naturally by the polymorphous distribution of many local environments. We illustrate this EBS approach for CdTe-HgTe, PbSe-SnSe and PbS-PbTe alloys. We found properties that are critical for e.g. topological phase transition and Rashba splitting but totally absent in conventional monomorphous approaches, including (1) co-existing, wavevector- and energy-dependent coherent band splitting and incoherent band broadening, (2) coherent-incoherent transition along different k space directions, and (3) Rashba-like band splitting having both coherent and incoherent features.