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[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

On 14 Mar 2006, at 17:50, yshtogun@cas.usf.edu wrote:

>  Dear All,
>   I tried to calculate band structure of carbon nanotubes in  
> external electric field (using barryopt 4). I meet problem with  
> number ob bands:
>
> initberry: ERROR -
>   In a finite electric field calculation, nband must be equal
>   to the number of valence bands.
>
>  Does somebody know why for electric field calculation nband must  
> be equal to the number of valence bands? Why does it work only for  
> valence bands? Is this restriction for electric field? Can I  
> calculate the band structure for all bands with electric field?

Dear Yaroslav,

If you look at the theory of the computations under electric field  
(see the references mentioned
in the tutorial on non-linear optics , section 3,
http://www.abinit.org/Infos_v4.6/Tutorial/lesson_nlo.html#3 )
you will see that the Kohn-Sham equation is modified by the presence  
of a d/dk operator, that
couple different k points, as well as different bands at different k  
points ! This is correctly
defined only for the Hilbert space spanned by an isolated group of  
bands. So, technically,
one cannot generalize easily the finite-electric field approach to  
the set of conduction bands,
that usually cannot be disentagled from all the higher-lying bands.

Well, there are two more fundamental problems, even with the valence  
bands :
- first the very well-known point that Kohn-Sham band structure  
should NOT be identified with
 the quasi-particle band structure (but everybody knows that usually  
one can rely on it, except for the gap)
- second the fact that the notion of band structure looses its  
meaning when
 a solid is placed in an electric field ! Indeed, an electric field  
corresponds to a linear potential
 in space, and there are no such things as Bloch states in an  
electric field - hence no band structure.
So, keep in mind that the quantity advertised as eigenenergies in the  
finite-field approach
implemented in ABINIT are formal, mathematical, quantities.

Of course, for sufficiently small fields, one might nevertheless  
examine long-lived resonances,
 and construct a  band structure relatively to a "not too large"  
region of space, where
 the electric field does not vary too much (see also the  
litterature, especially
 Nenciu's review paper).

But, nothing corresponding to this for the conduction states is  
implemented in ABINIT, and it is likely that
formal developments (to see how to get conduction band long-lived  
resonances energies from the finite-electric field
formalism) are needed before thinking to an implementation ...

Xavier