Band SrZrO.3 crystal

Fig. 3.3. Hartree-Fock energy bands for SrZrOs crystal...

Table 3.16. Band representations of upper valence bands in SrZrOs crystal induced from ...

As the third example of the band representations generated we consider SrZrO crystal. The configurations of valence electrons in free atoms are ... 

We shall illustrate the discussed procedure using the example of the SrZrOs crystal with the cubic perovskite structure. In Table 9.16 band representations of space group Oj induced by those atomic states that take part in the valence band formation are given. Each line of this table dehnes the connection of the q-basis for site-symmetry groups Oh Si), Dih 0) with the fe-basis at the symmetry points of BZ, see also Sect. 3.3. 

Table 9.21 gives the localization indices of Wannier functions in SrTiOs and SrZrOs crystals calculated for the valence bands by the method used in [63]. 

By construction, the BZ contains N allowed k vectors when N primitive nnit cells are included in the main region of a crystal. As the number N is assumed to be arbitrarily large, in the limiting case of N = oo the allowed k vectors take all values inside the BZ. In the electronic- structure calculations of crystals finite (and relatively small) numbers of k points are considered. However, the interpolation procedure used after calculation allows the one-electron energies to be shown as continuous functions of wavevectors (see, for example. Figures 3.3 3.5 for band structures of SrZrOs, MgO... 

Localized Wannier functions (LWFs) have been calculated for three upper valence bands in SrTiOs and SrZrOs, represented mainly by O 2p, Sr 4p, and O 2s atomic states (in the case of SrZrOs the last two bands overlap considerably). A total of 15 crystalline orbitals have been used to generate, correspondingly, 15 LWFs per primitive unit cell in both crystals under consideration, three oxygen atoms occupy the same Wyckoff positions, and four LWFs can be attributed to each oxygen atom. It was found by calculations with CRYSTAL03 code [23] that the centroids of four functions are positioned near the center of one oxygen (at distances of about 0.3 A). 

In all figures below the zero energy is taken at the Fermi level of the bulk crystal (SrZrOs or SrTiOs) and aU curves were shifted so that the centers of O Is bands... 

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