[Pw_forum] Band energy plots

Thu Jan 23 12:57:29 CET 2014

Thanks a lot for your reply. Your inputs did clear my doubts to a large
extent. I understand that I can get the band diagram using a 2-atom fcc
crystal. However, the next band diagram which I wanted to obtain contained
1 atom of Li as impurity in the 64 atom bulk Si. This system, I think can
not be broken down in a simpler system. So, what should I do in this case?

.....
Thanks,
Mitul Mundra
Final Year Dual Degree Student
Department of Chemical Engineering
IIT Kanpur, India.

On Thu, Jan 23, 2014 at 5:04 PM, Giovanni Cantele <
giovanni.cantele at spin.cnr.it> wrote:

>
> On 23 Jan 2014, at 11:46, Mitul Mundra <mitulm at iitk.ac.in> wrote:
>
> Hello,
>
> I am a beginner in using Quantum Espresso. I have a 64 atom Si supercell
> for which I am trying to plot band diagrams. I have gone through the
> tutorial "PWSCF: First Steps" available at
> http://www.fisica.uniud.it/~giannozz/QE-Tutorial/tutorial_pwscf_ex.pdf .
> The problem I am facing is that when I run a scf calculation using 4*4*4
> k-points, my output file has energies of 128 bands for every k-point. For
> example,
> *k = 0.0000 0.0000 0.0000 ( 12797 PWs)   bands (ev):*
>
> *    -5.6509  -4.5410  -4.5410  -4.5410  -4.5410  -4.5410  -4.5410
>  -3.5502*
> *    -3.5502  -3.5502  -3.5502  -3.5502  -3.5502  -3.5502  -3.5502
>  -3.5502*
> *    -3.5502  -3.5502  -3.5502  -3.2434  -3.2434  -3.2434  -3.2434
>  -1.3979*
> *    -1.3979  -1.3979  -1.3978  -1.3978  -1.3978  -1.2206  -1.2206
>  -1.2206*
> *    -1.2206  -1.2206  -1.2206  -1.2205  -1.2205  -1.2205  -1.2205
>  -1.2205*
> *    -1.2205  -0.5951  -0.5951  -0.5951  -0.5951   0.9797   0.9797
> 0.9797*
> *     0.9797   0.9797   0.9797   0.9797   0.9797   0.9797   0.9797
> 0.9797*
> *     0.9797   2.5385   2.5385   2.5385   2.5385   2.5385   2.5385
> 2.5385*
> *     2.5385   2.5385   2.5385   2.5385   2.5385   2.6504   2.6504
> 2.6504*
> *     2.6504   2.6504   2.6504   2.6504   2.6504   2.6504   2.6504
> 2.6504*
> *     2.6504   3.0031   3.0031   3.0031   3.0031   3.0031   3.0031
> 3.5849*
> *     3.5849   3.5849   3.5849   3.5849   3.5849   4.5713   4.5713
> 4.5713*
> *     4.5713   4.5713   4.5713   4.5713   4.5713   4.5713   4.5713
> 4.5713*
> *     4.5713   5.1567   5.1567   5.1567   5.1567   5.1568   5.1568
> 5.1568*
> *     5.1568   5.1568   5.1568   5.1568   5.1568   5.2932   5.2932
> 5.2932*
> *     5.2932   5.2932   5.2932   5.2932   5.2932   6.5240   6.5240
> 6.5240*
>
> On doing calculation = 'bands' and nbnd = 8, the output file contains
> energies of only 8 bands for every k-point which are the lowermost bands.
> *k = 0.0000 0.0000 0.0000     band energies (ev):*
>
> *    -5.6509  -4.5410  -4.5410  -4.5410  -4.5410  -4.5410  -4.5410
>  -3.5502*
> Then I run a bands.x executable to genrate bands.dat. On using plotband.x,
> I get the following.
>
> */opt/apps/espresso-5.0.1/bin/plotband.x*
> *Input file > bands.dat*
> *Reading    8 bands at     10 k-points*
> *Range:   -5.6510   -3.5500eV  Emin, Emax > -6, -3*
>
> *high-symmetry point:  0.0000 0.0000 0.0000   x coordinate   0.0000*
> *...*
>
> *high-symmetry point:  -0.5000-0.5000-0.5000   x coordinate   0.0000*
> *output file (xmgr) > si.bands.xmgr*
> *bands in xmgr format written to file si.bands.xmgr
>
>
>                                                                     *
> *output file (ps) > si.bands.ps <http://si.bands.ps/>*
> *Efermi > -3.987           *
> *deltaE, reference E (for tics) 1.0, -3.987*
> *n=           2           3*
> *  0.0000000E+00  0.0000000E+00*
> *  -5.651000      -5.581000    *
> * NaN            NaN    *
> ....
> ....
> ....
> and more NaNs and my *si.bands.ps <http://si.bands.ps/>* file contains no
> plot.
>
> I would be extremely thankful if someone could tell me where am I wrong
> and what different can I do to obtain the band plot (4 valence bands and 4
> conduction bands).
>
> Thanks,
> Mitul Mundra
> Final Year Dual Degree Student
> Department of Chemical Engineering
> IIT Kanpur, India.
>
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>
>
>
>
> If you want to obtain the “textbook” band plot of silicon (4 valence bands
> and 4 conduction bands) you CANNOT use a 64-atom supercell, but
> the 2-atom fcc unit cell of the silicon crystal.
>
> Whatever lattice you are using, a 64-atom supercell contains 4*64 valence
> electrons, corresponding to 2*64=128 occupied (valence) bands!
> That means that, even though you’re describing the silicon crystal just
> using a larger supercell (the textbook 2-atom fcc cell is the minimal choice
> among a set of infinite equivalent choices of the unit cell), you get
> EXACTLY the same band structure but described within the Brillouin zone
> of the lattice you are considering.
>
> So, let’s suppose that you choose  to replicate the Si fcc unit cell twice
> in each direction, thus using a 2x2x2 supercell, the Brillouin zone of this
> crystal is 1/2 x 1/2 x 1/2 = 1/8 smaller that the Brillouin zone of the
> crystal as described with the minimal cell.
> Because the electronic properties cannot depend on the choice of the unit
> cell, the silicon bands get folded into the smaller Brillouin zone.
> Plotting this band structure is possible, but of course you obtain many
> more bands, which are more difficult to handle with than the simpler
> Si band structure with only 4 valence bands. Therefore, the two band
> structures are DIFFERENT even though EQUIVALENT.
>
> To get rid of this difficulty, if you really want to describe bulk Si with
> your unit cell, you could firstly calculate the density of states (DOS),
> Indeed,
> being the DOS an integral over the Brillouin zone, the minimal and larger
> unit cell produce the SAME DOS with only a proportionality factor
> of difference (in my example above, the 2x2x2 cell will produce the 8
> times the DOS of the 1x1x1 unit cell). In this case comparing the two
> results is more straightforward.
>
> Giovanni
>
>
>
> --
>
> Giovanni Cantele, PhD
> CNR-SPIN
> c/o Dipartimento di Fisica
> Universita' di Napoli "Federico II"
> Complesso Universitario M. S. Angelo - Ed. 6
> Via Cintia, I-80126, Napoli, Italy
> e-mail: giovanni.cantele at spin.cnr.it
> Phone: +39 081 676910
> Skype contact: giocan74
>
> ResearcherID: http://www.researcherid.com/rid/A-1951-2009
> Web page: http://people.na.infn.it/~cantele
>
>
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