added overlap parameters, flag comp_angular_dep and ase in requirements

examples/carbons.py

@@ -0,0 +1,352 @@
+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()
+