Band structure of 2d materials, e.g., Graphene.

STEP 1

Optimized the lattice constant.

&CONTROL
    calculation='vc-relax'
    prefix='graphene'
    restart_mode='from_scratch'
    outdir='./outdir'
    pseudo_dir = '/BIGDATA1/ac_iphy_jrsun_1/soft/QE/SSSP'
    forc_conv_thr=1.0d-4
    etot_conv_thr=1.0d-6
/
&SYSTEM
    ibrav = 12, a = 2.460, b = 2.460, c= 20, cosab=-0.500000,
    nat = 2, ntyp = 1,
    ecutwfc = 40.0 ,
    ecutrho = 400.0 ,
    occupations = 'smearing', degauss = 0.0001, smearing = 'marzari-vanderbilt'
/
&ELECTRONS
    conv_thr = 1.0d-8,
    mixing_beta = 0.3,
/
&IONS
    ion_dynamics='bfgs'
/
&CELL
    press_conv_thr = 0.5D0
    cell_dynamics = bfgs,
    cell_dofree = '2Dxy'
/
ATOMIC_SPECIES
C 12.0107 C.pbe-n-kjpaw_psl.1.0.0.UPF
ATOMIC_POSITIONS crystal
C 0.000000000 0.000000000 0.250000000
C 0.333333333 0.666666667 0.250000000
K_POINTS automatic
12 12 1 0 0 0

New tags:

1. ibrav = 12

12          Monoclinic P, unique axis c     celldm(2)=b/a
                                             celldm(3)=c/a,
                                             celldm(4)=cos(ab)
      v1=(a,0,0), v2=(b*cos(gamma),b*sin(gamma),0),  v3 = (0,0,c)
      where gamma is the angle between axis a and b.

and if we use a, b, c, the unit is $\overset{\circ}{A}$.
2. press_conv_thr: Convergence threshold on the pressure for variable cell relaxation, and the default value is 0.5D0 Kbar.
3. cell_dofree = '2Dxy': only x and y components are allowed to change

And we find the relaxed structure file in .out file.

Begin final coordinates
     new unit-cell volume =    710.60309 a.u.^3 (   105.30051 Ang^3 )
     density =      0.37881 g/cm^3

CELL_PARAMETERS (alat=  4.64872629)
   1.002304830   0.000000000   0.000000000
  -0.501152415   0.868021445   0.000000000
   0.000000000   0.000000000   8.130081301

ATOMIC_POSITIONS (crystal)
C             0.0000000000        0.0000000000        0.2500000000
C             0.3333333330        0.6666666670        0.2500000000
End final coordinates

STEP 2

The self-consistent calculation.

&CONTROL
    calculation='scf'
    prefix='graphene'
    restart_mode='from_scratch'
    outdir='./outdir'
    pseudo_dir = '/BIGDATA1/ac_iphy_jrsun_1/soft/QE/SSSP'
/
&SYSTEM
    ibrav = 0, celldm(1) = 4.64872629
    nat = 2, ntyp = 1,
    ecutwfc = 40.0 ,
    ecutrho = 400.0 ,
    occupations = 'smearing', degauss = 0.0001, smearing = 'marzari-vanderbilt'
/
&ELECTRONS
    conv_thr = 1.0d-10,
    mixing_beta = 0.3,
/
ATOMIC_SPECIES
C 12.0107 C.pbe-n-kjpaw_psl.1.0.0.UPF
CELL_PARAMETERS alat
   1.002304830   0.000000000   0.000000000
  -0.501152415   0.868021445   0.000000000
   0.000000000   0.000000000   8.130081301
ATOMIC_POSITIONS crystal
C             0.0000000000        0.0000000000        0.2500000000
C             0.3333333330        0.6666666670        0.2500000000
K_POINTS automatic
12 12 1 0 0 0

Here we cancel the symmetry and use the structure file in the previous step.

STEP 3

The nscf calculation to obtain the more accurate Fermi energy.

Change the calculations to be nscf, and modify the k-mesh to be 24 24 1

Here the Fermi energy is -2.3461 eV in scf calculation and -2.3461 eV in nscf calculation, so 12,12,1 k-mesh is enough, so this step can be neglected.

STEP 4

Band structure calculations.

&CONTROL
    calculation='bands'
    prefix='graphene'
    restart_mode='from_scratch'
    outdir='./outdir'
    pseudo_dir = '/BIGDATA1/ac_iphy_jrsun_1/soft/QE/SSSP'
/
&SYSTEM
    ibrav = 0, celldm(1) = 4.64872629
    nat = 2, ntyp = 1,
    ecutwfc = 40.0 ,
    ecutrho = 400.0 ,
    occupations = 'smearing', degauss = 0.0001, smearing = 'marzari-vanderbilt'
/
&ELECTRONS
    conv_thr = 1.0d-10,
    mixing_beta = 0.3,
/
ATOMIC_SPECIES
C 12.0107 C.pbe-n-kjpaw_psl.1.0.0.UPF
CELL_PARAMETERS alat
   1.002304830   0.000000000   0.000000000
  -0.501152415   0.868021445   0.000000000
   0.000000000   0.000000000   8.130081301
ATOMIC_POSITIONS crystal
C             0.0000000000        0.0000000000        0.2500000000
C             0.3333333330        0.6666666670        0.2500000000
K_POINTS crystal_b
4
0.0000000000 0.000000000 0.000000000 30 ! G
-0.333333333 0.666666667 0.000000000 30 ! K
0.000000000 0.500000000 0.000000000 30 ! M
0.0000000000 0.000000000 0.000000000 30 ! G

STEP 5

post-processing from bands output using bands.x

&bands
outdir = './outdir'
prefix = 'graphene'
filband = 'graphene.bands.dat'
/

STEP 6

plot band using plotband.x

graphene.bands.dat
-25 12
graphene.bands.xmgr
graphene.bands.ps
-2.3461 
5 -2.3461 

HINT: This post-processing can not use parallel computing.

Here is the band structure of graphene, and we can find the Dirac point is located at K point.