[Wien] FS of a slab

[Artamonov Oleg]

Dear P.Blaha,

Thank you for suggestions. 
The "backfolding" idea is clear. One needs to retrieve the original k-point in the extended-zone scheme.
It is not so clear in the concept of "Bloch functions". Let’s consider the simplified problem and increase the unit cell size in z-direction by adding the vacuum space. One can do it in such a way that the reduced k-point range decreases ten times and one gets ten k-points in the original k-point range. I don’t understand how is it possible to solve that simplified problem by means of the analysis of the (QTLs) for atoms and interstitials.

Thanks in advance,
                                 Oleg Artamonov.


06.09.2011, 15:42, "Peter Blaha" <pblaha at theochem.tuwien.ac.at>:
>>      In the case of the super cell modeling the surface (few atom layers plus vacuum space) the size of the reciprocal lattice in the normal direction is small and the shape of the
>>      3D FS becomes a low-profile.
>>
>>      I need to get a distribution of E(*k*) in the k-vector-plane that is perpendicular to the surface plane in the real space.
>>
>>      Is Wien2k fit to that task?
>
> YES, and NO !
>
> NO, there is no automatic tool/method to do this.
>
> YES: all the information is there in principle. You have to understand
> "backfolding" and the concept of "Bloch functions".
>
> Backfolding: By doubling the unit cell in one dimension, you get at the
> Gamma point not only the Gamma eigenvalues of the original cell, but also
> the results from the X-point.....
>
> Now generalize this concept and if you treat the slab with 10 layers,
> you get 10-fold backfolding, i.e. it corresponds to a k-mesh with
> ten k-points between Gamma-X in the original cell.
>
> To identify which eigenvalue corresponds to which original k-perpendicular
> you use the "Bloch-function concept.
> i.e. on a Gamma point, psi_k(x+n.a) = psi_k(x)exp(ikn.a)
> This means on a "original Gamma point, the charge in all layers (neglecting surface
> effects) should be identical, for other k-points it should oszillate in a certain pattern.
> You can plot the partial charges (QTLs) as function of layer and check how it looks
> for the different states.
>
> In addition you can get surface states, which do not have a k_perp, but they
> should exponentially decay from the surface into the bulk.
>
> --
>
>                                       P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
> Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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