Fully Relativistic Layer-KKR Green Function Theory and Its Application to Spin-Polarized Photoemission
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Fully Relativistic Layer-KKR Green Function Theory and Its Application to Spin-Polarized Photoemission Eiiti Tamura Theoretische Festk6rperphysik, Universitiit Duisburg-GHD-4100Duisburg, Germany
ABSTRACT A fully relativistic layer-KKR formalism is developed for calculating the single-particle Green function in atomic layers parallel to crystalline surfaces of magnetic and nonmagnetic materials. Its application to spin-polarized photoemission is also discussed. INTRODUCTION In almost all surface spectroscopies, observed physical quantities are formulated through the surface Green function. The advantage of the Green-function formalism is not only that the perturbation can be handled systematically, but also that the spectral weight function (or the density of states) of the quasiparticles (or the ground-state electrons) can be obtained easily through the diagonal terms of the constructed Green function [1]. The layer-KKR Green function formalism [2] is one of the most powerful methods to obtain the surface (and also interface) Green function. Regarding a recent tendency to invent new materials which are often constructed on the surface, it is important to extend this formalism in order to cope with increasingly complex surface structures, i.e., including magnetic and high-atomic-number elements. In this paper the fully relativistic spin-polarized layer-KKR Green function theory is presented and applied to spin-polarized photoemission spectroscopy. RELATIVISTIC GREEN FUNCTION A semi-infinite crystal model may be viewed as a stack of atomic layers extending infinitely in two dimensions (x,y) parallel to the surface. The effective electron-solid interaction is approximated by a local, complex 2 x 2 potential matrix V(r) which is most generally described by the effective scalar and vector potentials v(r) and A(r) as Vr= (r v(r) ar- A(r)
a- .A(r) v(r)
()
where a- = (o-, a., az) are the Pauli spin operators. Since we confine our discussion to the ordered surfaces, the potential V(r) is two-dimensionally periodic and the surfaceparallel momentum kil, therefore, serves as a good quantum number. The surface barrier potential is either step-like or smooth (with image-potential asymptotic behavior) and may be understood as a topmost extra atomic layer. Consider the system in which a certain atomic layer is removed from the semi-infinite crystal, leaving an empty layer (V(r) = 0) sandwiched by the surface- and bulk-side atomic layers. The Green function for this system (the empty-layer Green function) can be expressed inside the empty layer as Gepty(r, r'; E, kil) = G+ (r, r'; E) + 1
(rIjR)
(E, kl)(jL,Ir')
'9'
Mat. Res. Soc. Symp. Proc. Vol. 253. -1992 Materials Research Society
(2)
348
where G' is the retarded free-propagating Green function given by f(r j,')(h G+(r, r'; E) = -2ik E '9
I.r')
for
r r'
)Or
(3)
The complex energy E is defined including the rest mass energy c2 and k = 1E - c4 /c. The free-propagating bispinor solutions Iz' and (z'l- (z J, h) are normalized as E C [z. (ndr) normIlize
(rlz)=
c2
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