[Wien] Slab dielectric function vs. bulk dielectric function

[Peter Blaha]

As you probably know, the dielectric function of Al converges VERY slowly
with respect to the k-mesh.

When you do slab calculations, you include the surface effect, but you also replace
the periodicity in k-z (and thus the k-mesh in k-z) to a backfoldung according to
your slab. Even a 39 ML slab corresponds probably not to a very large k-z mesh and
in addition the integration over k-z is limited to a "root"-sampling instead of the
tetrahedron method. I could even imagine large numerical problems in this 2-D integration
using a 3-D algorithm in joint due to large degeneracy of the tetrahedra.

At least you could differentiate between "integration problems" and surface effects
by using a 39-layer bulk structure (i.e. remove the vacuum in your supercell, so that
you get 3D-Al again, but restrict yourself to 1-k point in k-z) and compare the
resulting eps to bulk Al (with 1 atom/cell and good k-meshes.

Am 23.11.2013 16:54, schrieb phlhj phlhj:
> Dear all,
>
> I was trying to calculate the optical properties of Al(111) slab. For the bulk FCC Al, I can reproduce the dielectric functions and plasma frequency very precisely reported
> in literature before.  However, I did find some difference between the slab dielectric functions and the corresponding bulk values.
>
> Especially even though I used very thick slab, say 39MLs, in the low photo energy range (<1eV), the imaginary part is much larger than the bulk. I doubt this may be related
> to the band-folding and symmetry reduction in the direction normal to the surface.
>
> Also, I found the plasma frequency of the slab is smaller than the bulk plasma frequency.
>
> Mathematically, this behavior of the imaginary parts of the interband and intraband transitions contributions seems to be able to be understood from the f-sum rule.
>
> 1) However, physically it's hard to believe, because when the slab thickness is very thick for example the 39MLs used in my test calculation, the slab wavefunctions should
> be very very close to the bulk wavefunction except in the very thin slab/vacuum interface region. This should give us the dielectric functions for the slab which are very
> very close to the bulk values. This argument should be also true for the slab plasma frequency.
>
> 2) If the different values are because of the surface slab structure we used in the calculation, which indeed breaks the translational symmetry in the normal direction.
> Then the question is that in real experiment because the sample always is finite with the boundary surface, how can we get the dielectric information really for the ideal
> bulk rather than the slab similar as that mentioned above. Or in calculating dielectric function, when should we use bulk geometry? when should we use slab geometry?
>
> Thanks a lot for any idea.
>
> Wenmei
>
>
>
>
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>
>
>
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-- 
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
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