# [Pw_forum] The symmetry of bands

Dal Corso Andrea dalcorso at sissa.it
Fri Apr 3 14:36:39 CEST 2009

```On Fri, 2009-04-03 at 20:16 +0800, 程迎春 wrote:
> Dear dalcorso,
>       Thank you for your detailed reply.  The initial output I posted
> is not consistent with your output because I changed the
> "starting_magnetization=0.00," to 0.01. Though the energy is the same,
> the symmetry is different. I recalculate it with
> "starting_magnetization=0.00," and the output is same as your output.
>
>        In addition, I want to know how to calculate the exciton energy
> level ? Is that possible in recent pwscf?
>
As far as I know the answer is no. But maybe somebody else knows better
than me how to do this.

Andrea

> 2009/4/3 Dal Corso Andrea <dalcorso at sissa.it>
>
>         On my PC, with your input I obtain:
>
>          &plot nbnd=  30, nks=   1 /
>                    0.000000  0.000000  0.000000
>          -8.070  -8.070  -5.968  -5.968   1.092   1.092   6.154
>         6.154   6.169
>         6.169
>
>           6.802   6.802   6.816   6.816   7.016   7.016  11.136
>          11.136  13.603
>         13.603
>          17.514  17.514  18.094  18.094  18.118  18.118  19.967
>          19.967  20.042
>         20.042
>
>         That compare quite well with your bands:
>
>          &plot nbnd=  30, nks=   1 /
>                    0.000000  0.000000  0.000000
>          -8.070  -8.070  -5.968  -5.968   1.092   1.092   6.154
>         6.154   6.169
>         6.169
>           6.803   6.803   6.816   6.816   7.015   7.015  11.136
>          11.136  13.603
>         13.603
>          17.513  17.513  18.094  18.094  18.118  18.118  19.967
>          19.967  20.042
>         20.042
>
>
>         The output of bands.x says that the code is using the group
>         C_6v
>         to classify the bands
>
>                           xk=(   0.00000,   0.00000,   0.00000  )
>
>             double point group C_6v (6mm)
>             there are  9 classes and  3 irreducible representations
>             the character table:
>
>               E     -E     C2    2C3  -2C3   2C6  -2C6   3s_v  3s_d
>                           -C2                           -3s_v -3s_d
>         G_7    2.00 -2.00  0.00  1.00 -1.00  1.73 -1.73  0.00  0.00
>         G_8    2.00 -2.00  0.00  1.00 -1.00 -1.73  1.73  0.00  0.00
>         G_9    2.00 -2.00  0.00 -2.00  2.00  0.00  0.00  0.00  0.00
>
>         That has only three representations. An actally the .rap file
>         contains
>         only 1 2 or 3:
>
>          &plot_rap nbnd_rap=  30, nks_rap=   1 /
>                    0.000000  0.000000  0.000000    T
>
>               1       1       2       2       2       2       2
>         2       3
>         3
>               1       1       3       3       1       1       1
>         1       2
>         2
>               2       2       1       1       3       3       1
>         1       2
>         2
>
>         So the two bands 11-12 at 6.803 are 1 -> Gamma_7, the two
>         bands 13-14 at
>         6.816 are 3-> \Gamma_9 and
>         the two bands 15-16 7.015 are 1 -> \Gamma_7. The splitting is
>         13 meV and
>         0.199 meV in reasonable agreement with the APL that you
>         mention.
>
>         It seems that you have the correct bands but bands.x is not
>         using C_6v
>         to classify the bands.
>         Which is the output of bands.x?
>
>         Andrea
>
>
>
>
>         On Fri, 2009-04-03 at 11:10 +0800, 程迎春 wrote:
>         > Dear pwscf users,
>         >         I calculated band structure of  AlN considering
>         spin-orbital
>         > interaction.  Some published reports showed that considering
>         > spin-orbital interaction the top of valence band is split
>         into the
>         > Gamma7, Gamma9 and Gamma7 states by crystal field and
>         spin-orbital
>         > coupling (Appl. Phys. Lett. 83, 5163).  However, my
>         calculated band
>         > structure is different from the published one.  The
>         following is the
>         > input files:
>         > scf.in
>         > &control
>         >                     title = 2h_aln,
>         >                       prefix = '2h_band',
>         >                  calculation = 'scf' ,
>         >                 restart_mode = 'from_scratch' ,
>         >                   wf_collect = .false. ,
>         >                       outdir = './' ,
>         >                       wfcdir = './' ,
>         >                   pseudo_dir = './' ,
>         >                      tstress = .true. ,
>         >                      tprnfor = .true. ,
>         >                    wf_collect = .true. ,
>         >  /
>         >  &SYSTEM
>         >                        ibrav = 4,
>         >                    celldm(1) = 5.904838149212,
>         >                    celldm(3) = 1.603024550651,
>         >                          nat = 4,
>         >                         ntyp = 2,
>         >                      ecutwfc = 80,
>         >                        nosym = .false. ,
>         >                      lspinorb = .true.,
>         >                      noncolin= .true.,
>         >                    starting_magnetization=0.00,
>         >  /
>         >  &ELECTRONS
>         >             electron_maxstep = 100,
>         >                     conv_thr = 1.D-12,
>         >  /
>         > ATOMIC_SPECIES
>         >     N   14.00700  N.rel-pbe-rrkjus.UPF
>         >    Al   26.98200  Al.rel-pbe-rrkj.UPF
>         > ATOMIC_POSITIONS (crystal)
>         > N        0.333333333   0.666666667   0.379371803
>         > N        0.666666667   0.333333333   0.879371803
>         > Al       0.333333333   0.666666667  -0.002269507
>         > Al       0.666666667   0.333333333   0.497730493
>         > K_POINTS automatic
>         >   4 4 4   1 1 1
>         > band.in
>         > &control
>         >                       title = 2h_aln,
>         >                       prefix = '2h_band',
>         >                  calculation = 'bands' ,
>         >                 restart_mode = 'from_scratch' ,
>         >                   wf_collect = .false. ,
>         >                       outdir = './' ,
>         >                       wfcdir = './' ,
>         >                   pseudo_dir = './' ,
>         >  /
>         >  &SYSTEM
>         >                        ibrav = 4,
>         >                    celldm(1) = 5.904838149212,
>         >                    celldm(3) = 1.603024550651,
>         >                          nat = 4,
>         >                         ntyp = 2,
>         >                      ecutwfc = 80,
>         >                      occupations='fixed',
>         >                      nbnd=30,
>         >                          lspinorb = .true.,
>         >                      noncolin= .true.,
>         >                    starting_magnetization=0.00,
>         >  /
>         >  &ELECTRONS
>         >             electron_maxstep = 100,
>         >                     conv_thr = 1.D-12,
>         >  /
>         > ATOMIC_SPECIES
>         >     N   14.00700  N.rel-pbe-rrkjus.UPF
>         >    Al   26.98200  Al.rel-pbe-rrkj.UPF
>         > ATOMIC_POSITIONS (crystal)
>         > N        0.333333333   0.666666667   0.379371803
>         > N        0.666666667   0.333333333   0.879371803
>         > Al       0.333333333   0.666666667  -0.002269507
>         > Al       0.666666667   0.333333333   0.497730493
>         > K_POINTS
>         >          1
>         >   0.000000  0.000000  0.000000  1.00
>         >
>         > bands.in for bands.x to get band symmetry information
>         >
>         > &inputpp
>         > prefix='2h_band'
>         > outdir='./'
>         > filband='spin.dat'
>         > lsigma(3)=.true.
>         > lsym=.true.
>         > /
>         > The calculated results of the band structure at Gamma point
>         is as
>         > following:
>         > spin.dat:
>         >  &plot nbnd=  30, nks=   1 /
>         >             0.000000  0.000000  0.000000
>         >   -8.070  -8.070  -5.968  -5.968   1.092   1.092   6.154
>         6.154
>         > 6.169   6.169
>         >    6.803   6.803   6.816   6.816   7.015   7.015  11.136
>          11.136
>         > 13.603  13.603
>         >   17.513  17.513  18.094  18.094  18.118  18.118  19.967
>          19.967
>         > 20.042  20.042
>         >
>         > spin.dat.rap:
>         >  &plot_rap nbnd_rap=  30, nks_rap=   1 /
>         >             0.000000  0.000000  0.000000    T
>         >        1       2       5       6       5       6       5
>         6
>         > 3       4
>         >        1       2       3       4       1       2       1
>         2
>         > 5       6
>         >        5       6       1       2       3       4       1
>         2
>         > 5       6
>         >
>         > My questions are:
>         > 1. Why the calculated top of valence bands (15th, and 16th )
>         do not
>         > split as reported work (Appl. Phys. Lett.83,5163)?
>         > 2. In the spin.dat.rap file, what does the symbol "T" stand
>         for?  And
>         > what does the "1       2       5       6       5       6
>         5  ..."
>         > mean?
>         >
>         > Thank you in advance!
>         >
>         > --
>         > Y. C. Cheng
>         > Department of Physics
>         > Nanjing University
>         > Nanjing 210093
>         > P. R. China
>         > Tel: 86-25-83592907
>         > Email: yccheng.nju at gmail.com
>         >
>
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>
>         --
>         Andrea Dal Corso                    Tel. 0039-040-3787428
>         SISSA, Via Beirut 2/4               Fax. 0039-040-3787528
>         34014 Trieste (Italy)               e-mail: dalcorso at sissa.it
>
>
>
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>
>
>
> --
> Y. C. Cheng
> Department of Physics
> Nanjing University
> Nanjing 210093
> P. R. China
> Tel: 86-25-83592907
> Email: yccheng.nju at gmail.com
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--
Andrea Dal Corso                    Tel. 0039-040-3787428
SISSA, Via Beirut 2/4               Fax. 0039-040-3787528
34014 Trieste (Italy)               e-mail: dalcorso at sissa.it

```