[Pw_forum] Question about the band symmetry analysis in space group P63/mmc

[Qihang Liu]

Dear all,

I am struggling with the band symmetry analysis on a structure with a space
group #194 P63/mmc (D_6h^4). I use the tag space_group to define it so I
suppose the space group can be realized correctly by pwscf. As we know, the
little group of Gamma point should follow the group of the crystal
structure which is also D_6h. The the output of QE is D_3d. Please see the
following input and outputs:

scf.in
 &control
    prefix='bulk',
    pseudo_dir='./'
    outdir = './',
    wf_collect = .true.,
 /
 &system
    ibrav=  4,
    celldm(1)=   8.568018,  celldm(3)=   1.660013, space_group = 194
    nat=  3, ntyp= 3, nbnd = 48,
    ecutwfc = 36.0, ecutrho = 320.0,
    lspinorb = .true., noncolin = .true.,
    occupations='smearing', smearing='gaussian', degauss=0.02,
 /
 &electrons
  diagonalization='david',
  conv_thr = 1.0e-8,
  mixing_beta = 0.7,
 /
ATOMIC_SPECIES
  Li 6.941 Li.rel-pbe-s-kjpaw_psl.0.2.1.UPF
  Hg 200.5 Hg.rel-pbe-dn-kjpaw_psl.0.2.2.UPF
  As 74.922 As.rel-pbe-n-kjpaw_psl.0.2.UPF
ATOMIC_POSITIONS crystal_sg
Li  0.0000000000000000  0.0000000000000000  0.0000000000000000
Hg  0.3333333300000021  0.6666666699999979  0.2500000000000000
As  0.6666666699999979  0.3333333300000021  0.2500000000000000
K_POINTS automatic
  9 9 6 0 0 0

nscf.in
 &control
    calculation = 'nscf'
    prefix='bulk',
    pseudo_dir='./'
    outdir = './',
    wf_collect = .true.,
 /
 &system
    ibrav=  4,
    celldm(1)=   8.568018, celldm(3)=   1.660013, space_group = 194
    nat=  3, ntyp= 3, nbnd = 48,
    ecutwfc = 36.0, ecutrho = 320.0,
    lspinorb = .true., noncolin = .true.,
    occupations='smearing', smearing='gaussian', degauss=0.02,
 /
 &electrons
  diagonalization='david',
  conv_thr = 1.0e-8,
  mixing_beta = 0.7,
 /
ATOMIC_SPECIES
  Li 6.941 Li.rel-pbe-s-kjpaw_psl.0.2.1.UPF
  Hg 200.5 Hg.rel-pbe-dn-kjpaw_psl.0.2.2.UPF
  As 74.922 As.rel-pbe-n-kjpaw_psl.0.2.UPF
ATOMIC_POSITIONS crystal_sg
Li  0.0000000000000000  0.0000000000000000  0.0000000000000000
Hg  0.3333333300000021  0.6666666699999979  0.2500000000000000
As  0.6666666699999979  0.3333333300000021  0.2500000000000000
K_POINTS crystal_b
  3
  0 0 0 30  ! Gamma
  0 0 0.5 30 ! A
  0.5 0 0.5 1 ! L

bands.in
 &bands
    prefix  = 'bulk',
    outdir='./',
    filband = 'bands.dat',
    lsym = .true.,
 /

Output:
 **************************************************************************

                    xk=(   0.00000,   0.00000,   0.00000  )

     double point group D_3d (-3m)
     there are 12 classes and  6 irreducible representations
     the character table:

       E     -E    2C3   -2C3  3C2'  -3C2' i     -i    2S6   -2S6  3s_v
 -3s_v

G_4+   2.00 -2.00  1.00 -1.00  0.00  0.00  2.00 -2.00  1.00 -1.00  0.00
 0.00
G_5+   1.00 -1.00 -1.00  1.00  0.00  0.00  1.00 -1.00 -1.00  1.00  0.00
 0.00
G_6+   1.00 -1.00 -1.00  1.00  0.00  0.00  1.00 -1.00 -1.00  1.00  0.00
 0.00
G_4-   2.00 -2.00  1.00 -1.00  0.00  0.00 -2.00  2.00 -1.00  1.00  0.00
 0.00
G_5-   1.00 -1.00 -1.00  1.00  0.00  0.00 -1.00  1.00  1.00 -1.00  0.00
 0.00
G_6-   1.00 -1.00 -1.00  1.00  0.00  0.00 -1.00  1.00  1.00 -1.00  0.00
 0.00

Can anyone help me to explain the inconsistency? Is is related to some
non-symmophic symmetries that QE can not deal with? Thanks a lot.

Best,

Qihang Liu

Research Associate
Renewable and Sustainable Energy Institute (RASEI)
University of Colorado Boulder
Boulder, CO 80309-029 USA
https://www.colorado.edu/zunger-materials-by-design/qihang-liu
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