Orbital-based charge self-consistent Blackman-Esterling-Berk coherent potential approximation approach to substitutional disorder within a pseudopotential framework

We report the development of an ab initio electronic structure method applicable to generic substitutionally disordered real materials. A charge self-consistent orbital-based extension of the coherent potential approximation due to Blackman, Esterling, and Berk (BEB-CPA) is combined with the mixed-basis pseudopotential density functional theory approach. The general formalism in terms of a nonorthogonal basis set including subtleties of the pseudopotential framework is outlined. The BEB-CPA is validated on a binary tight-binding toy model against exact diagonalization of a randomly occupied cluster. Finally, the developed ab initio approach is benchmarked for a binary CuZn alloy, which confirms the robustness of the charge self-consistent procedure with respect to initial conditions.

Figure 1

Total density of states obtained within the BEB-CPA vs Lanczos method for binary alloy with fixed $c_A=0.4$, $c_B=0.6$, ${\epsilon }_A=-{\epsilon }_B=-4.0$, and $W^{AB}=W^{BA}=1.0$ at several species' diagonal hoppings.

Figure 2

Total density of states obtained within BEB-CPA vs Lanczos method with clusters removed from averaging for a binary alloy with fixed $c_A=0.4$, $c_B=0.6$, ${\epsilon }_A=-{\epsilon }_B=-4.0$, and $W^{AA}=W^{AB}=W^{BA}=W^{BB}=1.0$.

Figure 3

Schematic working flow of the ab initio program: In an inner self-consistency loop the CPA medium is calculated and in an outer loop a charge self-consistent Hamiltonian is achieved.

Figure 4

Total electronic density of states for ordered CuZn from DFT, for disordered ${\mathrm{Cu}}_{0.5}{\mathrm{Zn}}_{0.5}$ from charge self-consistent BEB-CPA, and from KKR-CPA after Ref. [14].

Figure 5

Evolution of the total electronic density of states for disordered ${\mathrm{Cu}}_{0.5}{\mathrm{Zn}}_{0.5}$ during the charge self-consistency cycle when starting from a wrong (Cu-derived) charge density at the Zn site. Shown are results for a specified number of iterations together with the charge self-consistent result from Fig. 4 (labeled scf).

Figure 6

(a) Total charge self-consistent Bloch spectral function $A(\omega ,\mathbf{k})$ of disordered ${\mathrm{Cu}}_{0.5}{\mathrm{Zn}}_{0.5}$ (false color) together with band structure of ordered CuZn (green); (b) projection on Cu-$d$ states; (c) projection on Zn-$d$ states.