Unhybridised £-bands

Fig.2.10. Self-consistent, fully hybridised energy-band structure for nonmagnetic chromium obtained as for tungsten and platinum, Figs.1.4,5. Comparison with the unhybridised bands in the previous figure gives a feeling for the accuracy one may obtain within the very simple unhybridised canonical band theory. It also gives an idea of the effect and importance of hybridisation, defined essentially as the difference between the two figures...

Fig.2.12. Fully hybridised energy-band structure for thallium as given in [2.6]. As in the case of chromium, comparison with the previous figure indicates the usefulness of the computationally simple unhybridised bands and the effect of hybridisation. Spin-orbit coupling has been neglected...

The description of the formation of energy bands contained in (2.28) and illustrated in Fig.2.7 constitutes a scaling principle according to which the unhybridised band structure of any close-packed solid of a given crystal structure may be synthesised from the same canonical bands. Hence, the unhybridised energy bands of all elemental metals with, for instance, fee structure may be obtained from the fee canonical bands shown in Fig.2.4 once their one-electron potentials (or potential parameters) are known. 

Fig.2.2b. The h + 1 diagonal elements of each subblock are the unhybridised or pure3 canonical bands.

Fig.2.8. Illustration of how the canonical bands i along one symmetry direction are transformed into unhybridised energy bands by the non-linear scaling prescribed by (2.12). The process is most easily understood if instead of the potential function P (E) one considers its inverse parametrised by (2.25)...

When hybridisation is taken into account by including structure constants with i il in the KKR-ASA equations (2.8), bands with similar symmetry labels are not allowed to cross and, instead, hybridisation gaps are created. This is the case of strong hybridisation. In addition, bands with similar symmetry labels which do not cross in the unhybridised case repel each other when hybridisation is included. This is called weak hybridisation. Several examples of these effects may be found in the comparison between unhybridised and fully hybridised band structures, i.e. between Figs.2.9,10 for Cr and between Figs. 2.11,12 for Tl. 

It is obvious that the effect of hybridisation, as seen for instance in Fig. 2.10, depends upon the relative position of the unhybridised energy bands. Therefore, it does not seem possible to define hybridised eanonieal bands which are independent of the potential and the lattice constant, and which can be transformed into hybridised energy bands simply by scaling. However, inspection of the KKR-ASA equations (2.8) reveals that the energy, lattice-parameter, and potential dependences enter only through the 4 potential functions P (E), Pp(E), P E), and Pf(E). Hence, if we regard the 4-dimensional vector P = P, P, P., P- as the independent variable we may, for s p or t... 

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