[Pw_forum] mos2

[ashkan shekaari]

Dear Ari,
Thank you so much for your great help.

On Wed, Apr 6, 2016 at 11:45 PM, Ari P Seitsonen <Ari.P.Seitsonen at iki.fi>
wrote:

>
> 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
>>
>>
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>>
>>
>>
>> --
>> Best regards,
>> Ashkan Shekaari
>> Plasma Physics Research Center, Science and Research Branch,
>> I A U, 14778-93855 Tehran, Iran.
>> Mobile: +98 (933) 459 7122
>>
>>
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-- 
*Best regards,*
*Ashkan Shekaari*
*Plasma Physics Research Center, Science and Research Branch, *
*I A U, **14778-93855 Tehran, Iran.*
*Mobile: +98 (933) 459 7122*
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