# [Pw_forum] The symmetry of bands

Dal Corso Andrea dalcorso at sissa.it
Fri Apr 3 10:14:20 CEST 2009

```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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