Relativistic single-site Green function for general potentials

Abstract

The fully relativistic single-site Green function is derived for generally shaped and magnetically polarized cell potentials. It is shown that the rightand left-hand-side (i.e. , ket and bra) solutions of the Dirac equations are the necessary ingredients and their generalized Wronskian relation provides important identities, which play a decisive role in the construction of the Green function.

Continuum random-phase approximation for relativistic point coupling models

“…Using the bracket notation of Dirac for the 2-dimensional spinors and following Ref. [33] we can express this Green's function as:…”

“…In the relativistic case the Dirac-equation in r-space depending on the quantum number κ is a two-dimensional equation and therefore the corresponding single particle Green's function is a 2×2 matrix. Using the bracket notation of Dirac for the 2-dimensional spinors we can write [33]:…”

“…In a first step, the ground state of the nucleus is determined by solving the self-consistent RMF equations (33) for the parameter set PC-F1 given in Table 1. The method we are using is a fourth order Runge-Kutta in r-space (Dirac-mesh) where nucleons move in a spherical box with radius R D = 15 fm and with a mesh size d D = 0.05 fm.…”

Relativistic spin-polarized KKR theory for superconducting heterostructures: Oscillating order parameter in the Au layer of Nb/Au/Fe trilayers

“…With integration over the angular parts and using the orthonormality of the Clebsch-Gordan coefficients and the following results [28] …”

“…The relativistic generalization of this theory-called DiracBogoliubov-de Gennes (DBdG) equations-was established by Capelle and Gross [20,21]. To be able to treat arbitrary geometries including semi-infinite geometries without the use of a giant supercell, in this paper we develop a relativistic spinpolarized screened Korringa-Kohn-Rostoker (KKR) method [22][23][24][25][26][27][28][29][30][31] for the solution of the DBdG equations. The KKR method was proven to be a very powerful tool over the last decade with a very broad range of possible applications (including impurities, disordered systems, magnetic response functions, magnetic anisotropy, pair interaction parameters, transport quantities, spectroscopy, etc.).…”