## Intensity map of unfolded spectral weight

The unfolded spectral weight can be visualized by an intensity map that the weight is smeared out by a Lorentian function:

where and are the magnitude of -vector in Bohr and energy in eV, respectively, and and are the corresponding degree of smearing. Note that the absolute value of the intensity map does not have physical meaning. The visualization can be performed by the following three steps:

(1) Compilation of intensity_map.c

In the the directory 'source', please compile 'intensity_map.c' as

  gcc intensity_map.c -lm -o intensity_map

and copy the executable file 'intensity_map' to your work directory.

(2) Generation of the intensity map

After finising the unfolding calculation, you can generate a file storing a mesh data for drawing the intensity map using 'intensity_map'. For the case of SiC () supercell in a two-dimensional honeycomb structure with a Si vacancy discussed in the previous subsection, where the input file is 'SiC_C_SP_V.dat', e.g., one can generate a file 'sic-intmap.txt ' storing the mesh data by

  ./intensity_map sic_c_sp_v.unfold_totup -c 3 -k 0.1 -e 0.1 -l -10 -u 6 > sic-intmap.txt

where the arguments have the following meaning:
  -c     column of spectral weight you analyze
-k     degree of smearing (Bohr^{-1}) in {\bf k}-vector
-e     degree of smearing (eV) in energy
-l     lower bound of energy for drawing the map
-u     upper bound of energy for drawing the map

You might be confused by the argument '-c' specifying the column number in the file. When you analyze 'System.Name.unfold_orbup(dn)', you will refer the sequence number for pseudo-atomic orbitals in 'System.Name.out'. Then, it should be noted that the number specified by '-c' is related to the sequence number for pseudo-atomic orbitals in 'System.Name.out' by .

(3) Drawing of the intensity map

Using gnuplot you can draw the intensity map. For example, for the calculation with the input file 'SiC_C_SP_V.dat' it can be done as follows:

  gnuplot> set yrange [-10.000000:6.000000]
gnuplot> set ylabel 'Energy (eV)'
gnuplot> set xtics('K' 0.000000,'G' 0.722259,'M' 1.347753,'K' 1.708883)
gnuplot> set xrange [0:1.708883]
gnuplot> set arrow nohead from 0,0 to 1.708883,0
gnuplot> set arrow nohead from 0.722259,-10.000000 to 0.722259,6.000000
gnuplot> set arrow nohead from 1.347753,-10.000000 to 1.347753,6.000000
gnuplot> set pm3d map
gnuplot> sp 'sic-intmap.txt'

Then, you may obtain a figure as shown in Fig. 63(a).