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* Graphene [#l124157c]
In this tutorial, the converge the Fermi level with respect to the number of k-points is discussed.

** Structural optimization [#qd7ae76d]
First of all, cell relaxation is performed by using "vc-relax" using the following input file

 &control
  calculation  = 'vc-relax'
  restart_mode = 'from_scratch',
  pseudo_dir   =  '/home/ikutaro/QE/pseudo',
  outdir       = './tmp'
  prefix       = 'gr'
  tstress      = .true.
  tprnfor      = .true.
 /
 &system
  ibrav       = 4
  A           = 2.46
  C           = 10.00
  nat         = 2
  ntyp        = 1
  ecutwfc     = 40.0
  ecutrho     = 400.0
  occupations = 'smearing'
  smearing    = 'mp'
  degauss     = 0.02
 /
 &electrons
  diagonalization = 'david'
  conv_thr        = 1.0e-12
  mixing_beta     = 0.5
 /
 &ions
 /
 &cell
  press          = 0.0d0
  press_conv_thr = 0.5d0
  cell_dofree    = 2Dxy
 /
 ATOMIC_SPECIES
  C  12.01070 c_pbe_v1.2.uspp.F.UPF
 ATOMIC_POSITIONS (crystal)
   C 0.0000000000000000 0.0000000000000000 0.0000000000000000
   C 0.3333333333333333 0.6666666666666667 0.0000000000000000
 K_POINTS (automatic)
  12 12 01 0 0 0
In this example, GBRV ultrasoft pseudopotential, cutoff energies of 40 and 400 Ry, and nonshifted 12 x 12 uniform k-point mesh is used. The vacuum of 10 Angstrom is inserted to separate periodic images. For the cell relaxation in two dimension, 'cell_dofree=2Dxy' is used.

** SCF and band structure calculations [#ee4c6c7d]
Having relaxed the cell parameters, let us start the band structure calculation.
In this tutorial, band structure calculations are performed by varying the k-point mesh in the SCF calculation to learn how the number of k-points or k-point density is crucial to determine the position of Fermi level and thereby the location of the Dirac point at the K point.
- SCF calculation
 &control
  calculation  = 'scf'
  restart_mode = 'from_scratch',
  pseudo_dir   =  '/home/ikutaro/QE/pseudo',
  outdir       = './tmp'
  prefix       = 'gr'
  tstress      = .true.
  tprnfor      = .true.
 /
 &system
  ibrav       = 4
  A           = 2.46575870
  C           = 10.00
  nat         = 2
  ntyp        = 1
  ecutwfc     = 40.0
  ecutrho     = 400.0
  occupations = 'smearing'
  smearing    = 'mp'
  degauss     = 0.02
  nbnd        = 8
 /
 &electrons
  diagonalization = 'david'
  conv_thr        = 1.0e-12
  mixing_beta     = 0.5
 /
 &ions
 /
 &cell
  press          = 0.0d0
  press_conv_thr = 0.5d0
  cell_dofree    = 2Dxy
 /
 ATOMIC_SPECIES
  C  12.01070 c_pbe_v1.2.uspp.F.UPF
 ATOMIC_POSITIONS (crystal)
   C 0.0000000000000000 0.0000000000000000 0.0000000000000000
   C 0.3333333333333333 0.6666666666666667 0.0000000000000000
 K_POINTS (automatic)
  12 12 01 0 0 0
- Band structure
 &control
  calculation  = 'bands'
  restart_mode = 'from_scratch',
  pseudo_dir   =  '/home/ikutaro/QE/pseudo',
  outdir       = './tmp'
  prefix       = 'gr'
  tstress      = .true.
  tprnfor      = .true.
 /
 &system
  ibrav       = 4
  A           = 2.46575870
  C           = 10.00
  nat         = 2
  ntyp        = 1
  ecutwfc     = 40.0
  ecutrho     = 400.0
  occupations = 'smearing'
  smearing    = 'mp'
  degauss     = 0.02
  nbnd        = 8
 /
 &electrons
  diagonalization = 'david'
  conv_thr        = 1.0e-12
  mixing_beta     = 0.5
 /
 &ions
 /
 &cell
  press          = 0.0d0
  press_conv_thr = 0.5d0
  cell_dofree    = 2Dxy
 /
 ATOMIC_SPECIES
  C  12.01070 c_pbe_v1.2.uspp.F.UPF
 ATOMIC_POSITIONS (crystal)
   C 0.0000000000000000 0.0000000000000000 0.0000000000000000
   C 0.3333333333333333 0.6666666666666667 0.0000000000000000
 K_POINTS (crystal_b)
 4
   0.00000000  0.00000000  0.00000000 20.0
   0.66666667 -0.33333333  0.00000000 20.0
   0.50000000  0.00000000  0.00000000 20.0
   0.00000000  0.00000000  0.00000000  0.0
In this example, the energy band is draw along the Gamma-K-M-Gamma line.
- Post-processing
To plot the band structure with gnuplot or alike, "bands.x" is used. Here's an example of the input file:
 &bands
  outdir  = './tmp'
  prefix  = 'gr'
  filband = 'gr.bands'
  lsym    = .true 
 /
With this input, "gr.bands.gnu" and "gr.bands.rap" are generated. For use with gnuplot, "gr.bands.gnu" can be used. One can use the following script ("band_plot.sh") to generate the band plot with gnuplot
 #!/bin/sh
 ef=`grep Fermi gr.scf.out | awk '{print $5}'`
 echo $ef
 gnuplot <<EOF
 ef=${ef}
 xmin=0.0
 xmax=1.5784
 ymin=-21.0
 ymax=4.0
 g1=0.0
 k=0.6671
 m=1.0007
 g2=1.5784
 offset=0.5
 set arrow from k,ymin to k,ymax nohead lt 0
 set arrow from m,ymin to m,ymax nohead lt 0
 unset xtics
 set xlabel 'E - E_F (eV)'
 set label '{/Symbol G}' at g1,ymin-offset center
 set label 'K' at k,ymin-offset center
 set label 'M' at m,ymin-offset center
 set label '{/Symbol G}' at g2,ymin-offset center
 set xrange [xmin:xmax]
 set yrange [ymin:ymax]
 set xzeroaxis lt 0
 plot 'gr.bands.gnu' using (\$1):(\$2-ef)
 pause -1
and type
 sh band_plot.sh
Here the output file for the corresponding SCF calculation is assumed to be "gr.scf.out."