[Pw_forum] Band energy plots

Thu Jan 23 12:34:37 CET 2014

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
> 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 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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