Andersen Group | El.-Phon. | QMC | C60 | GW | Resistivity saturation |
The GW Method |
Our interest has focussed on systems with stronger correlation. These are usually systems with rather localized orbitals, such as 3d- or 4f-orbitals. For these systems a plane wave expansion is impractical and we have therefore developed a GW method based on the LMTO band structure method.
The GW calculation requires the knowledge of the dielectric function. To obtain this function, we need to know the one-particle states over a rather large energy range. We have therefore extended the LMTO method to allow for the use of several orbitals per l- and m-quantum number ( Phys. Rev. B 49, 7219 (1994)). A method for calculating the dielectric function was then developed, where products of LMTO's were used to expand the dielectric function ( Phys. Rev. B 49, 16214 (1994)).
The local-field effects are expected to be large for systems with a strong variation in the charge density, like in Ni and NiO. The calculations for these 3d systems indeed show a large local-field effect on the static dielectric function but not on the loss function. We have demonstrated that the strength of the local-field effects depend on the magnitude of the self-interaction of a charge density resulting from a product of the orbitals involved in the important transitions. For the static dielectric function this is a 3d-3d product while for the loss function it is primarily a 3d-4f product. The latter product is small everywhere in space and the local-field corrections are therefore small in the loss function (Phys. Rev. B 50, 7311 (1994)).
The GW method was applied to NiO, which has become a model system for strongly correlated transition metal oxides. The LDA approximation fails for this system in the sense that it gives a much too small band gap and a too small magnetic moment. We have found that the GW method gives a good band gap and magnetic moment. It also improves the LDA description of the oxygen 2p band. It fails, however, to reproduced an experimentally observed satellite and it probably gives too much 3d character for the highest occupied states( Phys. Rev. Lett. 74, 3221 (1995)).
The GW method has also been applied to the 3d semi-cure states in certain semiconductors. These states have much too high energies in the LDA, but were shown to be rather well described in the GW approximation. The error in the LDA approximation was discussed ( Phys. Rev. B 54, 17564 (1996)).
The GW method has further been applied to alkali doped C_{60} compounds. The coupling to the low-lying t_{1u} plasmon at 0.5 eV was consider and the self-energy for the t1u band was calculated. The band width was found to be reduced by about 35 % due to this coupling. The source of the reduction was discussed ( J. Phys.: Cond. Matt. 9, 5635 (1997))). Effects beyond the GW approximation were further considered by using second and fourth order cumulant expansions. This expansion describes the development of multiple plasmon satellites and leads to a new broadening mechanism (Phys. Rev. B 50, 10462 (1994)).
The GW method has been reviewed in Rep. Prog. Phys. 61 , 237 (1998).
A list of some relevant publications is given here.
For further information contact Olle Gunnarsson (gunnar@and.mpi-stuttgart.mpg.de)
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