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 / [email protected] / 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 <[email protected]> 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 / [email protected] / 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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