[Pw_forum] mos2

[Ari P Seitsonen]

Dear Ashkan,

   First on your band structures, apparently you have aligned the zero of 
energy, on the vertical axis, somewhat differently. But overall, maybe 
they are correct. I guess that in the "super-cell" you refer the k points 
(Gamma, M, K) to the corresponding reciprocal lattice vectors, so that 
actually M_sc = 1/2 M_uc. And at K_sc you obtain the same gap as at K_uc, 
because the latter is actually K'_sc; shortly, K = (1/3,1/3,0) and K' = 
(-1/3,-1/3,0) = (2/3,2/3,0) (in units of the reciprocal lattice vectors), 
and since K_sc = 1/2 K_uc, also K'_sc = 1/2 K'_uc = K_sc. It might need a 
bit of drawing hexagons, before this become clear. :)

   Back-folding, since in a super-cell your lattice vectors in real space 
are longer, in reciprocal space they are correspondingly shorter (let us 
call them b1_sc and b2_sc). And since you have the periodicity also in the 
reciprocal space, the Brillouin zone is smaller and you have for 
example many more "Gamma points", Gamma_sc, in the original Brillouin 
zone of the "unit cell". So for example in your case, 2x2, b1_sc = 1/2 
b1_uc = M_uc. So you should obtain the same bands in the super-cell at the 
point Gamma_sc as M_uc. Thus I would see the bands at ca -1.6 and -2.1 eV 
at M_uc as the bands -1.3 and -1.7 eV at Gamma_sc. The band beginning at 
Gamma_uc and going toward 1/2 K_uc, that is also seen Gamma_sc-K_sc. And 
so on. But not only those, you see more bands because of the two 
two-dimensionality of your band structure.

   But to start understanding back-folding I would start by looking at a 
band structure in one dimension: You can take for example a cos(k) 
function, which mimics the dispersion of the s-type band (one can look up 
in a solid-state book why so). When you double the real-space unit cell, 
you can divide the reciprocal unit cell, so you cut the band at mid-point 
between the minimum at Gamma and maximum at X (if that is 1/2 b, you 
reciprocal lattice vector, or if you want to call it "M") and "fold it 
back", going away from the 1/2 X point toward Gamma again but with the 
same energy dependence as before: e(k) = e(X-k). Thus you get two bands in 
the new Brillouin zone, and they have the same energy at the point 1/2 X. 
Or you can go through the exercise of having a super-cell consisting of 
two atoms in the real-space cell, and when you make the atoms as 
identical, the band structure will be as the one of the super-cell, 
naturally.

   Well, this is certainly much more clearly explained in some text books 
or lecture notes. :)

     Greetings,

        apsi

PS Indeed, I would also learn how to use a consistent alignment of 
energies in the case of periodic systems with a band gap. Hint: Either 
mid-gap or top of valence band as the reference

-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
   Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935


On Wed, 6 Apr 2016, ashkan shekaari wrote:

> Dear Ari,
> I obtained the bands below via routine calculations (without back-folding). Is something wrong with my calculations?
> 
> What do you mean back-folding?
> 
> On Wed, Apr 6, 2016 at 9:30 PM, Ari P Seitsonen <Ari.P.Seitsonen at iki.fi> wrote:
>
>       Dear Ashkan,
>
>         Yes, due to back-folding - unless you perform the "back-folding". Jonas Björk told me that they have a public code for doing this and it should
>       also work with QE (I have not tried it myself though, even if I should have applied it recently - sorry Jonas!)
>
>           Greetings,
>
>              apsi
>
>       -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
>         Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
>           Ecole Normale Supérieure (ENS), Département de Chimie, Paris
>           Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935
> 
>
>       On Wed, 6 Apr 2016, ashkan shekaari wrote:
>
>             Dear QE users,
>             Does the 2*2 supercell of mos2 monolayer have a different band structure than that of the single unit cell?
> 
>
>             --
>             Best regards,
>             Ashkan Shekaari
>             Plasma Physics Research Center, Science and Research Branch, 
>             I A U, 14778-93855 Tehran, Iran.
>             Mobile: +98 (933) 459 7122
> 
> 
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://pwscf.org/mailman/listinfo/pw_forum
> 
> 
> 
> 
> --
> Best regards,
> Ashkan Shekaari
> Plasma Physics Research Center, Science and Research Branch, 
> I A U, 14778-93855 Tehran, Iran.
> Mobile: +98 (933) 459 7122
> 
>