Analysis of band structures

First, let us analyze how each band can be decomposed into each contribution of pseudo-atomic orbital in a band structure calculation for a primitive cell of SiC in a two-dimensional honeycomb structure without imperfection. Note that unfolding bands is not performed in this case. The SCF calculation for the primitive cell of the two-dimensional SiC can be performed as

  % mpirun -np 16 openmx SiC_Primitive.dat > sic_primitive.std & 
The input file 'SiC_Primitive.dat' can be found in the directory 'work/unfolding_example', and the basis functions and geometrical structure are specified as
  Species.Number       3
  C    C7.0-s2p2d1     C_PBE19
  Si   Si7.0-s2p2d1    Si_PBE19
  Te  Te11.0-s2p2d2f1  E

  Atoms.Number    3
  Atoms.SpeciesAndCoordinates.Unit  FRAC  # Ang|AU
  1  C    0.33333333   0.66666666   0.50000000   2.0  2.0
  2  Si   0.66666666   0.33333333   0.50000000   2.0  2.0
  3  Te   0.00000000   0.00000000   0.50000000   0.0  0.0

  Atoms.UnitVectors.Unit             Ang   # Ang|AU
  3.0690  0.0000000000   0.000
  -1.5345  2.6578319641   0.000
  0.0000  0.0000000000  10.000

where an empty atom having basis functions with a long tail is allocated at the center of the hexagon in order to improve description of conduction bands. Since the keyword 'Band.dispersion' is switched on as

  Band.dispersion              on       # on|off, default=off
  Band.Nkpath                   3
  60 0.33333333333 0.33333333333 0.00000000000  0.00000000000 0.00000000000 0.00000000000 K G
  52 0.00000000000 0.00000000000 0.00000000000  0.50000000000 0.00000000000 0.00000000000 G M
  30 0.50000000000 0.00000000000 0.00000000000  0.33333333333 0.33333333333 0.00000000000 M K
you might be able to plot the band dispersion using 'sic_primitive.BANDDAT1' as the solid line shown in Fig. 61(a). As for plotting the band dispersion, please refer the section 'Band dispersion'.

Figure 61: (a) Band structure of SiC primitive cell in a two-dimensional honeycomb structure without imperfection as shown in the inset, where the red line was obtained by the conventional calculation, and the green circles represent the total spectral weight. The radius reflects the magnitude of the weight. (b) Orbitally decomposed spectral weights of SiC primitive cell in a two-dimensional honeycomb structure without imperfection, where the green and purple circles represent the sum of spectral weights for the $s$, $p_x$, and $p_y$ orbitals, and the $p_z$ orbitals on the carbon atom, respectively. The radius reflects the magnitude of the weight. The calculation was performed by using an input file 'SiC_Primitive.dat' in the directory 'work/unfolding_example'.

Keywords relevant to analysis of band structure

For the calculation, the following keywords are also given as well

  Unfolding.Electronic.Band      on       # on|off, default=off
  Unfolding.LowerBound        -10.0       # default=-10 eV
  Unfolding.UpperBound          6.0       # default= 10 eV

  Unfolding.Nkpoint               4

  K 0.33333333333 0.33333333333 0.0000000000
  G 0.00000000000 0.00000000000 0.0000000000
  M 0.50000000000 0.00000000000 0.0000000000
  K 0.33333333333 0.33333333333 0.0000000000

  Unfolding.desired_totalnkpt    30

The specification of the keywords above are listed below.

Output files relevant to analysis of band structure

After getting the SCF convergence, the following files related to analyzing and/or unfolding bands will be generated.

By plotting both 'sic_primitive.BANDDAT1' and 'sic_primitive.unfold_totup' as
  gnuplot> set style data lines
  gnuplot> set zeroaxis
  gnuplot> set key below
  gnuplot> set ytics 1
  gnuplot> set mytics 5
  gnuplot> set xra [0.000000:1.708883]
  gnuplot> set yra [-10.0:6.0]
  gnuplot> set ylabel "eV"
  gnuplot> set xtics ("K" 0.000000, "G" 0.722258, "M" 1.347753, "K" 1.708882)
  gnuplot> p "sic_primitive.BANDDAT1","sic_primitive.unfold_totup" u 1:2:($3*0.02) w circle
one may obtain a figure as shown in Fig. 61(a), where the solid line and circle correspond to
"sic_primitive.BANDDAT1" and "sic_primitive.unfold_totup", respectively. The radius of the circle reflects the spectral weight, and all the radii are unity in this case, resulting in the equivalent radius for all the points, since we analyze the band dispersion represented by the Brillouin zone of the original cell.

Now let us move on 'sic_primitive.unfold_orbup' storing orbitally decomposed spectral weights. In a similar way above, one can plot the orbitally decomposed spectral weights as

  gnuplot> p "sic_primitive.BANDDAT1","sic_primitive.unfold_orbup" u 1:2:(($3+$4+$5+$6)*0.05) w circle,
  "sic_primitive.unfold_orbup" u 1:2:($7*0.05) w circle
Then, you may obtain a figure as shown in Fig. 61(b). In this case, the sum of spectral weights for the $s$, $p_x$, and $p_y$ orbitals, and the $p_z$ orbitals on the carbon atom are shown by the green and purple circles, respectively. It can be confirmed from the analysis that the $\sigma$ and $\pi$ bands are clearly distinguished. As for the format of 'sic_primitive.unfold_orbup', please refer the explanation above.