The paper is devoted to a numerical study of the dc electrical conductivity for ultra-thin metallic films. The cluster approach of Stein and Krey based on the quantum-mechanical Kubo formula is employed. The dc conductivity is obtained as a function of film roughness and thickness. The results indicate how the experimentally observed decrease and the 1 ML period of the resistivity vs. thickness curve can be related to the properties of the film surface.Numerische Berechnungen werden durchgefiihrt, um die statische elektrische Leitfahigkeit sehr dunner Metallschichten zu bestimmen. Es wird die von Stein und Krey vorgeschlagene, auf der quantenmechanischen Kubo-Formel basierende "Cluster"-Methode angewandt. Der elektrische Widerstand wird als Funktion der Oberflachenrauhigkeit und Schichtdicke erhalten. Die Resultate zeigen, wie die im Experiment beobachtete Abnahme und Periodizitat des dickenabhangigen Widerstands auf Eigenschaften der Oberflache bezogen werden konnen.
We present calculations of the dynamic susceptibility for a non-uniform ferromagnetic metal system with interatomic exchange included. The results obtained are general and can be applied t o ordered alloys, thin films, and other non-uniform media.We consider a system described by the Hamiltonian H =xtij aldajd + 7 u . n . n. -1 ~. . $ . 3 .where a:' is the creation operator for a n electron of spin 0 at the lattice site i, t.. is the hopping integral, U. is the intraatomic Coulomb integral, and J.. is the interatomic exchange integral: We assume the'system t o b e ferromagnetic but not necessarily translationally invariant.We aim at calculating the dynamical magnetic susceptibility. The tran9-v e r s e susceptibility is given by the Green function where spin operators on the right side are in Heisenberg picture and thermal average of the commutator is taken.The magnetic susceptibility of such a model was calculated for uniform media in RPA in /1/ and in another approximation in /2/. Our approximation is essentially similar but not identical t o the one used in /2/.
A simple quantum‐mechanical model is proposed of thin metallic film enabling one to calculate the static conductivity from the Kubo formula. The model takes into account only surface modifications of the film parameters. The validity of the results obtained for explaining experimental data is discussed.
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