[Pw_forum] Regarding Band Structure in primitive and conventional cell

[Giovanni Cantele]

On 23 Jun 2014, at 18:44, David Foster <davidfoster751 at yahoo.com> wrote:

> Dear Users
> Apologize for this simple question. Please guide me:
> I have used Si bulk for calculating its band gap. I used two approaches for doing it. One with ibrav=2 and working with primitive cell, and the other with ibrav=0
> and working with its conventional cell.
> For primitive I used following high-symmetric points:
> G: 0.0 0.0 0.0
> X: 0.5 0.0 0.5
> L: 0.5 0.5 0.5
> K: 0.375 0.375  0.75
> 
> and for conventional:
> G: 0.0  0.0  0.0
> X: 0.5  0.0   0.0
> M: 0.5  0.5  0.0
> R: 0.5  0.5  0.5
> 
> I got two different band structures.Conventional cell can be supposed as a supercell of its primitive, so, in the case of conventional, I thought I get only folded
> band structure. I have attached them.
> 
> Regards
> 
> David Foster
> 
> Ph.D. Student of Chemistry<conventional_BS.gif><primitive_BS.gif>_______________________________________________
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dear David,

what you should get is not the same band structure, but a band structure providing exactly the
same physical properties. Of course, because the simple cubic unit cell is 4 times larger than the ccc
unit cell, its BZ has a volume 4 time smaller. That is, the 4 occupied
bands of the ccc unit cell become 16 occupied bands in the sc cell, which is the folding you’re speaking about.
This being said, the folding is not that trivial as when you simply switch from a cubic crystal with side a to a cubic crystal with side 4a, because
in your case also the shapes of the BZs are different.

I’m not really convinced about the band structure of the simple cubic structure is correct. What are the basis atoms you use in that case?


I hope that I did not make any mistake, but for reference I attach the same calculation (path are just a little bit simpler than yours), were you can follow
the band “folding”, e.g. along the G-X direction, and recognise, in both cases, the LDA indirect (~0.5 eV) and direct (~2.5 eV) Si band gap. In your
conventional (simple cubic lattice) plot, I cannot see for example the direct gap at G
I also attach an image showing the two BZs.

Hope this helps,

    Giovanni








-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: http://people.na.infn.it/~cantele

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