[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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