<div dir="ltr">Dear Ari,<div>Thank you so much for your great help.</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Apr 6, 2016 at 11:45 PM, Ari P Seitsonen <span dir="ltr"><<a href="mailto:Ari.P.Seitsonen@iki.fi" target="_blank">Ari.P.Seitsonen@iki.fi</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br>
Dear Ashkan,<br>
<br>
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. :)<br>
<br>
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.<br>
<br>
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.<br>
<br>
Well, this is certainly much more clearly explained in some text books or lecture notes. :)<br>
<br>
Greetings,<br>
<br>
apsi<br>
<br>
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<div class="HOEnZb"><div class="h5"><br>
<br>
-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-<br>
Ari Paavo Seitsonen / <a href="mailto:Ari.P.Seitsonen@iki.fi" target="_blank">Ari.P.Seitsonen@iki.fi</a> / <a href="http://www.iki.fi/~apsi/" rel="noreferrer" target="_blank">http://www.iki.fi/~apsi/</a><br>
Ecole Normale Supérieure (ENS), Département de Chimie, Paris<br>
Mobile (F) : +33 789 37 24 25 (CH) : +41 79 71 90 935<br>
<br>
<br>
On Wed, 6 Apr 2016, ashkan shekaari wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
Dear Ari,<br>
I obtained the bands below via routine calculations (without back-folding). Is something wrong with my calculations?<br>
<br>
What do you mean back-folding?<br>
<br>
On Wed, Apr 6, 2016 at 9:30 PM, Ari P Seitsonen <<a href="mailto:Ari.P.Seitsonen@iki.fi" target="_blank">Ari.P.Seitsonen@iki.fi</a>> wrote:<br>
<br>
Dear Ashkan,<br>
<br>
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<br>
also work with QE (I have not tried it myself though, even if I should have applied it recently - sorry Jonas!)<br>
<br>
Greetings,<br>
<br>
apsi<br>
<br>
-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-<br>
Ari Paavo Seitsonen / <a href="mailto:Ari.P.Seitsonen@iki.fi" target="_blank">Ari.P.Seitsonen@iki.fi</a> / <a href="http://www.iki.fi/~apsi/" rel="noreferrer" target="_blank">http://www.iki.fi/~apsi/</a><br>
Ecole Normale Supérieure (ENS), Département de Chimie, Paris<br>
Mobile (F) : +33 789 37 24 25 (CH) : +41 79 71 90 935<br>
<br>
<br>
On Wed, 6 Apr 2016, ashkan shekaari wrote:<br>
<br>
Dear QE users,<br>
Does the 2*2 supercell of mos2 monolayer have a different band structure than that of the single unit cell?<br>
<br>
<br>
--<br>
Best regards,<br>
Ashkan Shekaari<br>
Plasma Physics Research Center, Science and Research Branch, <br>
I A U, 14778-93855 Tehran, Iran.<br>
Mobile: +98 (933) 459 7122<br>
<br>
<br>
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<br>
<br>
<br>
--<br>
Best regards,<br>
Ashkan Shekaari<br>
Plasma Physics Research Center, Science and Research Branch, <br>
I A U, 14778-93855 Tehran, Iran.<br>
Mobile: +98 (933) 459 7122<br>
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</blockquote>
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