Dear Ari, Thank you so much for your great help. On Wed, Apr 6, 2016 at 11:45 PM, Ari P Seitsonen <ari.p.seitso...@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.seitso...@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.seitso...@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.seitso...@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@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 >> >> > _______________________________________________ > Pw_forum mailing list > Pw_forum@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*
_______________________________________________ Pw_forum mailing list Pw_forum@pwscf.org http://pwscf.org/mailman/listinfo/pw_forum