Fully relativistic multiple scattering calculations for general potentials

The formal basis for fully relativistic Korringa-Kohn-Rostoker (KKR) or multiple scattering calculations for the electronic Green function in case of a general potential is discussed. Simple criteria are given to identify situations that require to distinguish between right- and left-hand-side solutions to the Dirac equation when setting up the electronic Green function. In addition, various technical aspects of an implementation of the relativistic KKR for general local and nonlocal potentials will be discussed.

Figure 1

Unit cell of a hcp solid with two different choices of the coordinate system. In both cases, the $z$ axis points out of the plane.

Figure 2

Wave-function coupling scheme for the atom shown in Fig. 1 at the origin with the magnetization along the $\widehat{z}$ direction in the spin-angular representation, i.e., the rows and columns are indexed with $\mathrm{\Lambda }=(\kappa ,\mu )$ given for a maximum angular momentum $l_{\max }=2$. The subblocks denoted by $s_{1/2}$ and so on correspond to $\kappa =+1,-1,+2,-2$, and $+3$. Within each subblock, the magnetic quantum number $\mu$ runs from $-j$ to $+j$ with $j=\left|\kappa \right|-\frac{1}{2}$. For each column, the occurring letter indicates the nonvanishing contributions ${\varphi }_{{\mathrm{\Lambda }}^{\prime }\mathrm{\Lambda }}(\mathbf{r},z)$ to the sum ${\sum }_{{\mathrm{\Lambda }}^{\prime }}{\varphi }_{{\mathrm{\Lambda }}^{\prime }\mathrm{\Lambda }}(\mathbf{r},z)$. All columns having the same letter contribute to a corresponding subblock of the $t$ matrix.