Subband structure of graphene nanoribbons

Tools

• Create GNR atom coordinates using ASE

8-ZGNR using grid

• zgnr_grid.py:

from gpaw import GPAW, FermiDirac
from ase import Atoms
from ase.io import read, write
from gpaw import GPAW, PoissonSolver, Mixer
from ase.structure import graphene_nanoribbon


# -------------------------------------------------------------
# Bulk configuration
# -------------------------------------------------------------

zgnr = graphene_nanoribbon(8, 1, type='zigzag', saturated=True,
                            C_H=1.1, C_C=1.42086, vacuum=8.0,
                            magnetic=False, initial_mag=0.0)

zgnr.center()
write('zgnr.traj', zgnr)


# Make self-consistent calculation and save results
calc = GPAW(h=0.18,
            mode='fd',
            xc='PBE',
            basis='szp(dzp)',
            kpts=(1,1,9),
            maxiter=600,
            occupations=FermiDirac(width=0.05, maxiter=2000),
            mixer=Mixer(beta=0.010, nmaxold=8, weight=100.0),
            poissonsolver=PoissonSolver(eps=1e-12),
            txt='band_sc.txt')

zgnr.set_calculator(calc)
zgnr.get_potential_energy()
calc.write('band_sc.gpw')


# Calculate band structure along Gamma-X 

from ase.dft.kpoints import ibz_points, get_bandpath
#points = ibz_points['fcc']
#G = points['Gamma']
#X = points['X']
G = (0, 0, 0)
X = (0, 0, 0.5)
kpts, x, X = get_bandpath([G, X], zgnr.cell, 60)

calc = GPAW('band_sc.gpw',
            mode='fd',
            kpts=kpts,
            txt='band_harris.txt',
            fixdensity=True,
            maxiter=600,
            parallel={'domain': 1},
            eigensolver='cg', # 'cg' is allowed for grid method only
            usesymm=None,
            convergence={'bands': 100})
#           convergence={'bands': 'all'})
if calc.input_parameters['mode'] == 'lcao':
    calc.scf.reset()

calc.get_potential_energy()
ef = calc.get_fermi_level()
calc.write('band_harris.gpw')

calc = GPAW('band_harris', txt=None)
import numpy as np

eps_skn = np.array([[calc.get_eigenvalues(k,s)
                     for k in range(60)]
                    for s in range(1)]) - ef



# Write the results to a file e.g. for plotting with gnuplot
f = open('bands.dat', 'w')
for n in range(66):
    for k in range(60):
        print >>f, k, eps_skn[0, k, n]
    print

8-ZGNR using LCAO

• zgnr_lcao.py:

from gpaw import GPAW, FermiDirac
from ase import Atoms
from ase.io import read, write
from gpaw import GPAW, PoissonSolver, Mixer
from ase.structure import graphene_nanoribbon 


# -------------------------------------------------------------
# Bulk configuration
# -------------------------------------------------------------

zgnr = graphene_nanoribbon(8, 1, type='zigzag', saturated=True,
                            C_H=1.1, C_C=1.42086, vacuum=8.0,
                            magnetic=False, initial_mag=0.0)

zgnr.center()
write('zgnr.traj', zgnr)


# Make self-consistent calculation and save results
calc = GPAW(h=0.18,
            mode='lcao',
            xc='PBE',
            basis='szp(dzp)',
            kpts=(1,1,9),
            occupations=FermiDirac(width=0.05, maxiter=2000),
            mixer=Mixer(beta=0.010, nmaxold=8, weight=100.0),
            poissonsolver=PoissonSolver(eps=1e-12),
            txt='band_sc.txt')

zgnr.set_calculator(calc)
zgnr.get_potential_energy()
calc.write('band_sc.gpw')


# Calculate band structure along Gamma-X 
from ase.dft.kpoints import ibz_points, get_bandpath
G = (0, 0, 0)
X = (0, 0, 0.5)
kpts, x, X = get_bandpath([G, X], zgnr.cell, 60)

calc = GPAW('band_sc.gpw',
            mode='lcao',
            xc='PBE',
            basis='szp(dzp)',
            kpts=kpts,
            txt='band_harris.txt',
            fixdensity=True,
            parallel={'domain': 1},
            usesymm=None,
            convergence={'bands': 'all'})

if calc.input_parameters['mode'] == 'lcao':
    calc.scf.reset()

calc.get_potential_energy()
calc.write('band_harris.gpw')

• find_band_dat.py

from ase.lattice import bulk
from gpaw import GPAW

calc = GPAW('band_harris', txt=None)
import numpy as np

eps_skn = np.array([[calc.get_eigenvalues(k,s)
                     for k in range(60)]
                    for s in range(1)]) + 6.23712

for n in range(66):
    for k in range(60):
        print k, eps_skn[0, k, n]
    print