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/
> --------------------------------------------------------------------------
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
