On Jul 14, 2012, at 7:34 AM, yavar pour azar wrote: > Dear QE users, > > I have a conceptual problem with k-point sampling in supercells. > > Suppose we have a simple cubic unit cell for the bulk, which it's electronic > structure, total energy and etc... is calculated by n*n*n BZ Sampling. > for example I can see band width and band curvature along k axis, and i will > have max and min points for every band in different k_points such gamma, X, > L,...... > > Now, if we want to make a n*n*n supercell from this unit cell, it is the > known fact that just gamma point calculations is enough. > > Anyone can see following sentences in most QE tutorials; > "Increase supercell in real space by a factor N along a ; EXACTLY same > results obtained by reducing divisions in k mesh (in the new smaller BZ) by > factor N" > > This is the problem that I cant understand : when we substitute the unit cell > by n*n*n supercell ( k=0), the calculated bands with new sampling has no > curvature and extension along k axis, because we have just a K point. Total > Energy, probably is same as former unit cell (by integer factor), but if we > will lose information about other aspects of electronic structure by this > sampling? > I would appreciate it if anyone can help me to understand this, or refer me > to a source. > > > > PS: suppose supercell sustained no relaxation or similar changes, and we > have just the two different scales from one infinite, periodic lattice. > > > > Thanks in advance. > > Yavar Taghipour Azar > PhD student > Physics Group, AEOI, Tehran, Iran > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum
If you build your supercell correctly, of course no information will be lost. Reverting to the example you did --namely, the same cubic structure simulated by using either a 1x1x1 unit cell with an NxNxN sampling or an NxNxN supercell with a 1x1x1 sampling of the BZ-- you should consider that the band structure you plot in both cases is along a path in the BZ that has NOTHING to do, in principle, with the sampling of the BZ itself. The BZ sampling controls the convergence of the calculated properties (the ground-state charge density, for example) with respect to the BZ integration. The path along the BZ you use for band structure calculations is instead just a collection of k-points inside the BZ which you choose in order to plot the band structure of a system. Of course, for the NxNxN supercell you expect to get a number of bands which is NxNxN times that of the 1x1x1 calculation: this is the so called band structure folding. That means that your band structure, even though apparently different, is just the same but described within a BZ which is NxNxN times smaller than for the 1x1x1 unit cell. In conclusion, even for the NxNxN supercell, if you select a path in the BZ, you'll find the same electronic bands, gaps, curvature, even though described within a different BZ. Giovanni -- **** PLEASE NOTICE THE NEW E-MAIL ADDRESS: giovanni.cantele at spin.cnr.it Giovanni Cantele, PhD CNR-SPIN c/o Dipartimento di Scienze Fisiche Universita' di Napoli "Federico II" Complesso Universitario M. S. Angelo - Ed. 6 Via Cintia, I-80126, Napoli, Italy Phone: +39 081 676910 Skype contact: giocan74 ResearcherID: http://www.researcherid.com/rid/A-1951-2009 Web page: http://people.na.infn.it/~cantele http://www.nanomat.unina.it -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20120717/b8b1179a/attachment.htm
