All-electron KKR Calculations for Metallic Systems with Thousands of Atoms Per Cell via Sparse Matrix Iterative Solvers

To perform electronic-structure calculations for inherently large systems, such as a quantum dots with heterogeneous interfaces, we must perform the calculations over very large unit cells (10$^{4}$ to 10$^{8}$ atoms). KKR methods typically solve for G by direct inversion G$^{-1}$, with known analytic form. Using a screened, k-space hybrid KKR, we solve Dyson's equation for the Green's function using a reference state via G = G$_{ref}$ [ I - (t - t$_{ref}$) G$_{ref}$]$^{-1}$, scattering matrices t and t$_{ref}$ are known and the non-Hermitian tensor G$_{ref}$ is chosen for convenience and sparsity [1]. The approach is O(N) for bandgap materials, whereas it is O(N$^2$) for metals but with a potentially large prefactor. We use Krylov-space solvers to reduce storage and exploit known symmetries. Parallel iterative and energy contour solves are made also. We explore the numerical efficiency and scaling versus atoms per unit cells. \newline [1] Smirnov and Johnson, Comp! $^1$Phys. Comm. 148, 74-80 (2002).