[Wien] metal supercell band folding dielectric function

[MingWenmei]

Thank you, Professor Pblaha.
What you said is true only for semiconductors, because they have finite band gap separating "valence bands" from "conduction bands" and this will not change even with band folding from larger supercell calculations. 
However, for metals, because around Fermi energy the bands are partially occupied, then some states from the SAME band in primary unit cell calculation might fold back to bands with DIFFERENT band index.  
The simplest example is say we have a metal with one single band of parabolic dispersion when do an "unit cell" calculation. When we do dielectric function calculation, we only have the INTRA band contribution, that is, Drude-like dielectric function, which is only determined by plasma frequency and damping parameter.
This means all states are from one single band. However when we do a cell of 2 times the unit cell, then basically we will have TWO bands due to band folding. The INTRA band contribution won't change because the plasma frequency is the same. However in this case we will have INTER band transition contributing to the dielectric function. This is something extra compared to ONE band calculation. It means the dielectric function will depend on the cell you are choosing. Physically this is WRONG.
Thank you for your suggestion,
Wenmei



> Date: Sat, 30 Mar 2013 08:27:39 +0100
> From: pblaha at theochem.tuwien.ac.at
> To: wien at zeus.theochem.tuwien.ac.at
> Subject: Re: [Wien] metal supercell band folding dielectric function
> 
> a) Do an optics calculation for the same 32 atom Au-supercell, but without dopant,
> just "label" one Au atom by "Au1", so that the symmetry is identical to your Cd-doped
> calculation. This should give identical eps2 than the small Au calculation (beware of
> k-mesh effects !!!)
> b) Use bandstructure with "fat-bands" and partial DOS for analysis of your doped system.
>     You can also run optics with matrix-elements restricted to eg. only Cd or only Au
>     (missing crossterms). See UG for details.
> 
> Am 30.03.2013 00:27, schrieb MingWenmei:
> > Dear all,
> >
> > I am calculating the interband dielectric function of Au with low concentration of Cd dopant (say 1/32 atom concentration). Very strikingly in low energy (< 1eV) range,
> > there appears a high peak (~a few hundred). However for FCC pure gold, the interband dielectric function is very small (around zero) below 1eV.
> >
> > So my question is physically why the dielectric function changes this dramatically? I did the band structure calculation. I found within small energy range (<1eV) of Fermi
> > energy for the doped system, there are some extra bands. I began to realize it is this small energy difference of the bands above Fermi energy that causes the high peak of
> > dielectric function.
> >
> > These extra bands may be from doped Cd and also may be from the band-folding of host Au in the supercell calculation. The contribution from supercell itself to the
> > dielectric peak seems not to make sense physically. For if band-folding can affect the value of dielectric function, then even for pure FCC Au we may get significantly
> > different dielectric functions by choosing "unit cell" of different size (say 1x1x1, 4x4x4 times primary cell )
> >
> > Could anyone give some comment to understand this?
> >
> > Thank you a lot,
> >
> > Wenmei
> >
> >
> >
> >
> >
> >
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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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