import matplotlib.pyplot as plt
import numpy as np
from nanonet.tb import get_k_coords
import nanonet.tb as tb
# --------------------- vectors (in Angstroms) --------------------
lat_const = 1.42
a1 = 0.5 * lat_const * 3
a2 = 0.5 * lat_const * np.sqrt(3)
period = np.array([[a1, a2, 0.0],
[a1, -a2, 0.0]])
# --------------------------- wave vectors -------------------------
lat_const_rec = 2 * np.pi / (3 * np.sqrt(3) * lat_const)
special_k_points = {
'GAMMA': [0, 0, 0],
'K': [lat_const_rec * np.sqrt(3), lat_const_rec, 0],
'K_prime': [lat_const_rec * np.sqrt(3), -lat_const_rec, 0],
'M': [lat_const_rec * np.sqrt(3), 0, 0]
}
sym_points = ['GAMMA', 'M', 'K', 'GAMMA']
num_points = [25, 25, 25]
k_points = get_k_coords(sym_points, num_points, special_k_points)
# ------------------------------------------------------------------
fig_counter = 1
def graphene_first_nearest_neighbour():
coords = """2
Graphene
C1 0.00 0.00 0.00
C2 {} 0.00 0.00
""".format(lat_const)
# --------------------------- Basis set --------------------------
s_orb = tb.Orbitals('C')
s_orb.add_orbital("pz", energy=0, orbital=1, magnetic=0, spin=0)
# ------------------------ set TB parameters----------------------
t = 2.8
tb.set_tb_params(PARAMS_C_C={'pp_pi': t})
# --------------------------- Hamiltonian -------------------------
h = tb.Hamiltonian(xyz=coords, nn_distance=1.5)
h.initialize()
h.set_periodic_bc(period)
band_structure = np.zeros((sum(num_points), h.h_matrix.shape[0]))
for jj, item in enumerate(k_points):
band_structure[jj, :], _ = h.diagonalize_periodic_bc(item)
# visualize
global fig_counter
plt.figure(fig_counter)
fig_counter += 1
ax = plt.axes()
ax.set_title(r'Band structure of graphene, 1st NN')
ax.set_ylabel('Energy (eV)')
ax.plot(np.sort(band_structure), 'k')
ax.plot([0, band_structure.shape[0]], [0, 0], '--', color='k', linewidth=0.5)
plt.xticks(np.insert(np.cumsum(num_points) - 1, 0, 0), labels=sym_points)
ax.xaxis.grid()
plt.show()
def radial_dep(coords):
"""
Step-wise radial dependence function
"""
norm_of_coords = np.linalg.norm(coords)
if norm_of_coords < 1.5:
return 1
elif 2.5 > norm_of_coords > 1.5:
return 2
elif 3.0 > norm_of_coords > 2.5:
return 3
else:
return 100
def graphene_third_nearest_neighbour_with_overlaps():
"""
All parameters are taken from Reich et al, Phys. Rev. B 66, 035412 (2002)
Returns
-------
"""
coords = """2
Graphene
C1 0.00 0.00 0.00
C2 {} 0.00 0.00
""".format(lat_const)
# --------------------------- Basis set --------------------------
s_orb = tb.Orbitals('C')
s_orb.add_orbital("pz", energy=-0.28, orbital=1, magnetic=0, spin=0)
# ------------------------ set TB parameters----------------------
gamma0 = -2.97
gamma1 = -0.073
gamma2 = -0.33
s0 = 0.073
s1 = 0.018
s2 = 0.026
tb.set_tb_params(PARAMS_C_C1={'pp_pi': gamma0},
PARAMS_C_C2={'pp_pi': gamma1},
PARAMS_C_C3={'pp_pi': gamma2},
OV_C_C1={'pp_pi': s0},
OV_C_C2={'pp_pi': s1},
OV_C_C3={'pp_pi': s2})
# --------------------------- Hamiltonian -------------------------
h = tb.Hamiltonian(xyz=coords, nn_distance=3.1, comp_overlap=True)
h.initialize(radial_dep)
h.set_periodic_bc(period)
band_structure = np.zeros((sum(num_points), h.h_matrix.shape[0]))
for jj, item in enumerate(k_points):
band_structure[jj, :], _ = h.diagonalize_periodic_bc(item)
# visualize
global fig_counter
plt.figure(fig_counter)
fig_counter += 1
ax = plt.axes()
ax.set_title('Band structure of graphene, 3d NN \n after Reich et al, Phys. Rev. B 66, 035412 (2002)')
ax.set_ylabel('Energy (eV)')
ax.plot(np.sort(band_structure), 'k')
ax.plot([0, band_structure.shape[0]], [0, 0], '--', color='k', linewidth=0.5)
plt.xticks(np.insert(np.cumsum(num_points) - 1, 0, 0), labels=sym_points)
ax.xaxis.grid()
plt.show()
def graphene_nanoribbons_zigzag():
from ase.build.ribbon import graphene_nanoribbon
from ase.visualize.plot import plot_atoms
atoms = graphene_nanoribbon(11, 1, type='zigzag')
period = np.array([list(atoms.get_cell()[2])])
period[:, [1, 2]] = period[:, [2, 1]]
coord = atoms.get_positions()
coord[:, [1, 2]] = coord[:, [2, 1]]
coords = []
coords.append(str(len(coord)))
coords.append('Nanoribbon')
for j, item in enumerate(coord):
coords.append('C' + str(j+1) + ' ' + str(item[0]) + ' ' + str(item[1]) + ' ' + str(item[2]))
coords = '\n'.join(coords)
s_orb = tb.Orbitals('C')
s_orb.add_orbital("pz", energy=-0.28, orbital=1, magnetic=0, spin=0)
# ------------------------ set TB parameters----------------------
gamma0 = -2.97
gamma1 = -0.073
gamma2 = -0.33
s0 = 0.073
s1 = 0.018
s2 = 0.026
tb.set_tb_params(PARAMS_C_C1={'pp_pi': gamma0},
PARAMS_C_C2={'pp_pi': gamma1},
PARAMS_C_C3={'pp_pi': gamma2},
OV_C_C1={'pp_pi': s0},
OV_C_C2={'pp_pi': s1},
OV_C_C3={'pp_pi': s2})
# --------------------------- Hamiltonian -------------------------
h = tb.Hamiltonian(xyz=coords, nn_distance=3.1, comp_overlap=True)
h.initialize(radial_dep)
h.set_periodic_bc(period)
k_points = np.linspace(0.0, np.pi/period[0][1], 20)
band_structure = np.zeros((len(k_points), h.h_matrix.shape[0]))
for jj, item in enumerate(k_points):
band_structure[jj, :], _ = h.diagonalize_periodic_bc([0.0, item, 0.0])
# visualize
ax = plt.axes()
ax.set_title('Graphene nanoribbon, zigzag 11')
ax.set_ylabel('Energy (eV)')
ax.set_xlabel(r'Wave vector ($\frac{\pi}{a}$)')
ax.plot(k_points, np.sort(band_structure), 'k')
ax.xaxis.grid()
plt.show()
ax1 = plot_atoms(atoms, show_unit_cell=2, rotation='90x,0y,00z')
ax1.axis('off')
plt.show()
def graphene_nanoribbons_armchair():
from ase.build.ribbon import graphene_nanoribbon
from ase.visualize.plot import plot_atoms
atoms = graphene_nanoribbon(11, 1, type='armchair')
period = np.array([list(atoms.get_cell()[2])])
period[:, [1, 2]] = period[:, [2, 1]]
coord = atoms.get_positions()
coord[:, [1, 2]] = coord[:, [2, 1]]
coords = []
coords.append(str(len(coord)))
coords.append('Nanoribbon')
for j, item in enumerate(coord):
coords.append('C' + str(j+1) + ' ' + str(item[0]) + ' ' + str(item[1]) + ' ' + str(item[2]))
coords = '\n'.join(coords)
s_orb = tb.Orbitals('C')
s_orb.add_orbital("pz", energy=-0.28, orbital=1, magnetic=0, spin=0)
# ------------------------ set TB parameters----------------------
gamma0 = -2.97
gamma1 = -0.073
gamma2 = -0.33
s0 = 0.073
s1 = 0.018
s2 = 0.026
tb.set_tb_params(PARAMS_C_C1={'pp_pi': gamma0},
PARAMS_C_C2={'pp_pi': gamma1},
PARAMS_C_C3={'pp_pi': gamma2},
OV_C_C1={'pp_pi': s0},
OV_C_C2={'pp_pi': s1},
OV_C_C3={'pp_pi': s2})
# --------------------------- Hamiltonian -------------------------
h = tb.Hamiltonian(xyz=coords, nn_distance=3.1, comp_overlap=True)
h.initialize(radial_dep)
h.set_periodic_bc(period)
k_points = np.linspace(0.0, np.pi/period[0][1], 20)
band_structure = np.zeros((len(k_points), h.h_matrix.shape[0]))
for jj, item in enumerate(k_points):
band_structure[jj, :], _ = h.diagonalize_periodic_bc([0.0, item, 0.0])
# visualize
ax = plt.axes()
ax.set_title('Graphene nanoribbon, armchair 11')
ax.set_ylabel('Energy (eV)')
ax.set_xlabel(r'Wave vector ($\frac{\pi}{a}$)')
ax.plot(k_points, np.sort(band_structure), 'k')
ax.xaxis.grid()
plt.show()
ax1 = plot_atoms(atoms, show_unit_cell=2, rotation='90x,0y,00z')
ax1.axis('off')
plt.show()
def graphene_nanotube():
from ase.build.tube import nanotube
from ase.visualize.plot import plot_atoms
n = 10
m = 10
atoms = nanotube(n, m)
atoms.wrap()
period = np.array([list(atoms.get_cell()[2])])
period[:, [1, 2]] = period[:, [2, 1]]
coord = atoms.get_positions()
coord[:, [1, 2]] = coord[:, [2, 1]]
coords = []
coords.append(str(len(coord)))
coords.append('Nanoribbon')
for j, item in enumerate(coord):
coords.append('C' + str(j + 1) + ' ' + str(item[0]) + ' ' + str(item[1]) + ' ' + str(item[2]))
coords = '\n'.join(coords)
# --------------------------- Basis set --------------------------
s_orb = tb.Orbitals('C')
s_orb.add_orbital("pz", energy=0, orbital=1, magnetic=0, spin=0)
# s_orb.add_orbital("py", energy=0, orbital=1, magnetic=1, spin=0)
# s_orb.add_orbital("px", energy=0, orbital=1, magnetic=-1, spin=0)
# ------------------------ set TB parameters----------------------
t = 2.8
tb.set_tb_params(PARAMS_C_C={'pp_pi': t})
# --------------------------- Hamiltonian -------------------------
h = tb.Hamiltonian(xyz=coords, nn_distance=1.7, comp_angular_dep=False)
h.initialize()
h.set_periodic_bc(period)
k_points = np.linspace(0.0, np.pi/period[0][1], 20)
band_structure = np.zeros((len(k_points), h.h_matrix.shape[0]))
for jj, item in enumerate(k_points):
band_structure[jj, :], _ = h.diagonalize_periodic_bc([0.0, item, 0.0])
# visualize
ax = plt.axes()
ax.set_title('Band structure of carbon nanotube, ({0}, {1}) \n 1st nearest neighbour approximation'.format(n, m))
ax.set_ylabel('Energy (eV)')
ax.set_xlabel(r'Wave vector ($\frac{\pi}{a}$)')
ax.plot(k_points, np.sort(band_structure), 'k')
ax.xaxis.grid()
plt.show()
ax1 = plot_atoms(atoms, show_unit_cell=2, rotation='10x,50y,30z')
ax1.axis('off')
plt.show()
if __name__ == '__main__':
graphene_first_nearest_neighbour()
graphene_third_nearest_neighbour_with_overlaps()
graphene_nanoribbons_zigzag()
graphene_nanoribbons_armchair()
graphene_nanotube()