Sorry, I already realize I've made a proofreading mistake: 'use X for the reciprocal "short" direction, X' for the reciprocal "long" direction, and M as the vector composition of both X and X'. The reciprocal "short" direction is parallel to the surface unit cell "long" direction, correct?'
should instead read: 'use X for the reciprocal "long" direction, X' for the reciprocal "short" direction, and M as the vector composition of both X and X'. The reciprocal "short" direction is parallel to the surface unit cell "long" direction, correct?' apologies. On Thu, Jun 6, 2013 at 10:08 AM, Abraham Hmiel <[email protected]> wrote: > Hello again Hatuey, > > Yes, the k-band utility from Bilbao will give you the band paths for the > bulk. For a surface, it is indeed a little different but not really any > more difficult. The question you asked is not especially relevant to > SIESTA, but I will answer it anyway because it's a good pedagogical example. > > I am using this paper as a sample reference for your case: > http://www.cmdmc.com.br/redecmdmc/lab/arquivos_publicacoes/2781_Density%20Functional%20Theory%20Study%20on%20the%20Structural%20and%20Electronic%20Properties%20of%20Low%20Index.pdf > -- they are dealing with composite TiO2//SnO2 rutile surfaces but in the > same Miller index planes that you are interested in, and also TiO2 and SnO2 > individually so it makes for a good example. Usually it is a good idea to > adopt the conventions of previously published research, especially if you > are making direct comparisons to them. > > Draw your attention to pages 8948 and 8949 where they depict the > calculated band structure. They also show the Brillouin zone of the > surface. The surface Brillouin zone ought to be a rectangle for this > material because we are dealing with a cubic crystal cut along a face > diagonal, so one dimension of the surface Brillouin zone will be longer > than the other. The labels M and X, now, are NOT the same as the bulk M and > X high-symmetry points. > > Consider the (110) plane case: If you make a cut to the bulk crystal along > (110) and then orient your viewpoint so that [110] is normal to your line > of sight (the z-direction, like in your simulation), one choice of lattice > vectors that yield a rectangular surface unit cell is: {1 -1 0} and {0 0 > 1}. You are probably already using this in your surface unit cell. The > paper, and its predecessor on which the label conventions are based ( > http://prb.aps.org/pdf/PRB/v64/i7/e075407) use X for the reciprocal > "short" direction, X' for the reciprocal "long" direction, and M as the > vector composition of both X and X'. The reciprocal "short" direction is > parallel to the surface unit cell "long" direction, correct? So now, for > the SnO2 rutile (110) case, we arrive at the conclusion that X is along [0 > 0 1] and X' is along [1 -1 0], and M is along [1 -1 1]. Pretty simple, > right? But we're not done because we need to tell SIESTA what to do with > this information and it doesn't care about the bulk crystal, just the > surface unit cell for the purposes of finding reciprocal lattice vectors > and so on. In this unit cell, the x direction is along [0 0 1], and the > y-direction is along [1 -1 0] in the bulk crystal. > > We need to remember that the 1st Brillouin zone's boundary is half the > length of the reciprocal cell vectors (see > http://upload.wikimedia.org/wikipedia/commons/2/22/Brillouin_zone.svg for > a graphical example), so, for the surface unit cell of (110) Rutile SnO2: > The Gamma point is at [0 0 0] (that's easy) > The X' point is at [0 0.5 0] (because it's parallel to the y-direction, > the reciprocal short direction) > The M point is at [0.5 0.5 0] (because it's the sum of vectors X' and X, > therefore x+y unit vectors) > The X point is at [0.5 0 0] (again, the x-direction in the surface unit > cell, the reciprocal long direction) > > And then, creating this path in reciprocal space in a way SIESTA can > understand (and I'm estimating the number of points in each line): > > WriteBands .true. > BandLinesScale ReciprocalLatticeVectors > > %block BandLines > 1 0 0 0 \Gamma > 20 0.5 0 0 Xprime > 50 0.5 0.5 0 M > 20 0 0.5 0 X > 50 0 0 0 \Gamma > %endblock BandLines > > Then, run: (assuming your systemlabel is "SnO2_110") > bash>> gnubands < SnO2_110.bands > SnO2_110_bands.dat > > When plotted with software like matplotlib or gnuplot, this should create > a plot that is similar to figure 2b in the 1st reference I gave you once > you choose the correct viewing window. Keep in mind that your energies will > be with respect to the program's energy zero and not the VBM, Fermi energy, > or vacuum level unless you write a script to subtract that energy from the > second column of SnO2_110_bands.dat. > > If you calculate the lengths of each reciprocal lattice vector in 1/bohr > or Angstrom you can probably make a more consistent band lines scale than > the one I used above for the number of points along each line, but I'll > leave that as an exercise for you. Also another exercise for you: do you > have to change anything in the SIESTA .fdf that I've shown you above if you > want to print the bandlines for SnO2 (101) instead of (110)? Why or why > not? > > I hope this helped! Also, I believe I'm fully correct, but if you perform > the calculation and find any errors, let me know and we can continue the > conversation. > > Best of luck, > > > > On Thu, Jun 6, 2013 at 7:52 AM, Hatuey Hack <[email protected]>wrote: > >> Dear **Abraham, >> >> Thank you very much for the very useful information! >> >> In the link from the Bilbao Crystallographic Server, I got the k-vectors >> for the bulk Brillouin zone, right? I am not seen (understand) how, from >> them, I can determine the k-points (and then the path) in a given plane, >> for example, for the (110) plane. >> >> I think (but I may be wrong) that if I put a path from the bulk when >> calculating the surface, I will waste computing resource, and some bands in >> the direction perpendicular to the plane will be null or flat. >> >> Regards, >> >> Hatuey >> >> ------------------------------ >> >> *On Wed, Jun 5, 2013 at 10:19 PM, Abraham Hmiel <[email protected]>wrote: >> Hi Hatuey,* >> >> What you're looking for is here: http://www.cryst.ehu.es/** >> cryst/get_kvec.html <http://www.cryst.ehu.es/cryst/get_kvec.html> - find >> the space group for SnO2 and enter it in the box. The k-vector coordinates >> that SIESTA uses in a band structure calculation are in the first set of >> columns, "CDML." If you input coordinates this way, it is important to use >> "BandlinesScale ReciprocalLatticeVectors" in your .fdf file. >> >> Then, the manual page http://www.icmab.es/leem/** >> siesta/Documentation/Manuals/**siesta-3.1-manual/node55.html<http://www.icmab.es/leem/siesta/Documentation/Manuals/siesta-3.1-manual/node55.html> >> **for information on how to define the path in k-space which will of >> course be implemented in your .fdf file. >> >> Defining the path in k-space has no implications for the density of >> states calculation. I always use the projected density of states output >> options, as I have a lot more control over what orbitals I'm looking at for >> my own analysis. That particular page is here: http://www.icmab.es/** >> leem/siesta/Documentation/**Manuals/siesta-3.1-manual/**node60.html<http://www.icmab.es/leem/siesta/Documentation/Manuals/siesta-3.1-manual/node60.html> >> >> With PDOS, it is usually a good idea to have a finer k-grid than your SCF >> calculation. For example, if you are simulating a surface with a converged >> k-grid of: >> >> %block kgrid_Monkhorst_pack >> 6 0 0 0.0 >> 0 6 0 0.0 >> 0 0 1 0.0 >> %block kgrid_Monkhorst_pack >> >> The following k-grid may be suitable for a PDOS calculation: >> >> %block PDOS.kgrid_Monkhorst_pack >> 16 0 0 0.0 >> 0 16 0 0.0 >> 0 0 1 0.0 >> %block PDOS.kgrid_Monkhorst_pack >> * >> De:* Hatuey Hack <[email protected]> >> *Para:* "[email protected]" <[email protected]> >> *Enviadas:* Quarta-feira, 5 de Junho de 2013 11:17 >> *Assunto:* defining k path for surfaces >> >> Dear all, >> >> I am trying to calculate the band structure for different 2D systems. My >> systems consist in nanosheets of SnO2 obtained in the 101 and 110 direction >> from a tetragonal structure "grown" in the xy plane with the vacum in the z >> direction. >> >> I would like to know how to define the k path in the Brillouin zone for >> electronic band and DOS calculation. >> >> Best regards, >> >> Hatuey >> >> >> > > > -- > *Abraham Hmiel* > Katherine Belz Groves Fellow in Nanoscience > Xue Group, College of Nanoscale Science and Engineering at SUNY Albany > http://abehmiel.net/about > > -- *Abraham Hmiel* Katherine Belz Groves Fellow in Nanoscience Xue Group, College of Nanoscale Science and Engineering at SUNY Albany http://abehmiel.net/about
