[Wien] Electric Field Effects

[Paul Fons]

Thank you for your quick help with my electric field question.  I have a couple of other related questions that I am still puzzled about.

The first question is the applicability of the Berry phase approach.  From what I understand, the Berry phase approach is usually couched within the density functional perturbation theory paradigm, e.g. in the limit of small E fields.  In fact, in the paper you co-authored with Stahn [PRB v63, 165205 (2001)] you actually mentioned the Berry Phase. 

   "For a quantum-mechanical description of 'polarization in a crystal' a geometrical Berry's phase approach as been introduced in recent years.  Unfortunately, this approach is only valid if there is no external electric field in the crystal, which means that the surfaces of the crystal are short circuited."

As the fields we are interested in are fairly large (a factor of ten below the dielectric breakdown voltage), I was not confident about the applicability of a perturbative Berry's phase approach.   It was for this reason, I thought that your supercell approach (with the introduction of a vacuum slab at the kink and the fixing of the end atoms to prevent surface relaxation) would be a good approach that could be used even for moderately strong fields (0.01-0.1 V/Angstrom = 0.2-2 mRy).  I also noted that in the same paper above, it was stated that calculations at artificially larger fields were necessary to ensure enough numerical precision.  In the paper values of 200 times the experimental field values were used (e.g. 1400 kV/mm = 14 V/Angstrom = 2 mRy) to ensure that there was enough numerical precision in the answer as "for numerical reasons, the accuracy of the calculated potential Vint is of the order of the maximum potential applied".  Is this still the case for the latest revision of the Wien code (Wien12)?

Let me close, by thanking you again for your time.  I hope my questions are not too naive and can help others as well.  I hope to see you in Tokyo next month.

Best Wishes,
			Paul Fons



On Aug 6, 2012, at 11:59 PM, Peter Blaha wrote:

> It depends a bit on what you are looking for.
> We were interested in GaAs and the relative change of positions of Ga and As atoms
> under the E-filed.
> For this question such large cells are necessary, because in this setup we had 2 kinks
> and the relaxations near the kink are very much influenced by them.
> 
> In fact, nowadays I would do it differently, namely exactly as you have in mind:
> 
> In a slab geometry (surface) one can make this kink in the vacuum region and we have now
> even asymmetric fields, so that you can put the strong variation into the vacuum.
> 
> In any case, as far as I remember it was a tedious work.
> 
> Better approaches are now done using a "Berry"-phase method and as far as I know, Oleg Rubel
> (rubelo at tbh.net) has such an approach programmed into WIEN2k.
> 
> Am 06.08.2012 16:38, schrieb Paul Fons:
>> Hi All,
>> 	I have been studying the work of Stahn, Pietsch, Blaha, and Schwartz on electric field induced charge density variations (in GaAs) [PRB v63, 165205 (2001).  I had a couple of quick questions.  In the paper a large (22 formula units) of GaAs is used and the field is inverted halfway across the cell in the z-direction (e.g. to maintain the periodic boundary conditions).  I am curious to know if such a large number of repeats is necessary or is it simply necessary to have the field applied over a minimum spatial length.  First, what is the case for GaAs, can the number of repeats be varied without large changes in the result?  The second question has more to do with the sort of systems I wish to calculate E-field-induced effects upon.  They are already quite large in size with about 20 layers in a supercell and I would like to avoid making the cell unnecessarily large.  Would it make sense to make a vacuum layer between two units cells (and leave the electrostatic inflection!
> po
>>  int there).  I assume I would have to fix the positions of the atoms at the end of the cell next to the vacuum layer if I did this.  Does this make sense?  Any advice on what cell sizes would be appropriate would be gratefully received.
>> 
>> 				Paul Fons
>> _______________________________________________
>> Wien mailing list
>> Wien at zeus.theochem.tuwien.ac.at
>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>> 
> 
> -- 
> 
>                                      P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
> 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