vor_m = Voronoi(rec_moire_lattice)
sorted_vertices = np.array(
sorted(vor_m.vertices, key=lambda x: np.abs(x.view(complex))))
k_point = sorted_vertices[0]
# Calculate the wavefunction
hamiltonian = bandcalc.calc_hamiltonian(rec_moire_lattice, potential_matrix, m)
wavefunction = bandcalc.calc_wave_function_on_grid(k_point, rec_moire_lattice,
grid, hamiltonian,
energy_level)
# Energies for reference
energies, prefix = bandcalc.get_unit_prefix(
np.sort(
np.linalg.eigvals(
bandcalc.calc_hamiltonian(rec_moire_lattice, potential_matrix,
m)(k_point))))
energy_slice = energies[energy_level -
5 if energy_level - 5 > -1 else None:energy_level +
5 if energy_level + 5 < len(energies) else None]
energy = np.real(energies[energy_level])
#np.save("wavefunction_moire_{}deg_energy_level_{}_shells_8.npy".format(angle, energy_level), wavefunction)
# Plot the results
fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(11, 5))
bandcalc.plot_lattice(axs[0], rec_moire_lattice, "ko")
axs[0].text(0.05,
0.95,
hamiltonian = bandcalc.calc_hamiltonian(rec_moire_lattice, potential_matrix,
mass)
## Calculate MBZ and choose some K-points for the k-path
vor_m = Voronoi(rec_moire_lattice)
sorted_vertices = np.array(
sorted(vor_m.vertices, key=lambda x: np.abs(x.view(complex))))[:6]
sorted_vertices = np.array(
sorted(sorted_vertices, key=lambda x: np.angle(x.view(complex))))
points = np.array([[0, 0], sorted_vertices[0], sorted_vertices[1],
sorted_vertices[3]])
k_names = [r"$\gamma$", r"$\kappa'$", r"$\kappa''$", r"$\kappa$"]
path = bandcalc.generate_k_path(points, N)
## Calculate bandstructure
bandstructure, prefix = bandcalc.get_unit_prefix(
bandcalc.calc_bandstructure(path, hamiltonian))
sorted_bandstructure = np.sort(bandstructure)
fig, ax = plt.subplots(nrows=7, ncols=2, figsize=(7, 20))
for i in range(7):
## Calculate the wannier function
R = 1 / 3 * (moire_lattice[5] + moire_lattice[3] +
moire_lattice[6]).astype(np.float32)
r = 5 * bandcalc.generate_monkhorst_pack_set(m, 80)
wannier_function = bandcalc.calc_wannier_function_gpu(hamiltonian,
k_points,
rec_moire_lattice,
r,
R,
sorted(vor_m.vertices, key=lambda x: np.abs(x.view(complex))))[:6]
sorted_vertices = np.array(
sorted(sorted_vertices, key=lambda x: np.angle(x.view(complex))))
points = np.array([[0, 0], sorted_vertices[0], sorted_vertices[1],
sorted_vertices[3]])
path = bandcalc.generate_k_path(points, N)
k_names = [r"$\gamma$", r"$\kappa'$", r"$\kappa''$", r"$\kappa$"]
## Calculate the band structure
# The bandstructure is slightly different from the bandstructure in the
# original paper, but that is most likely just a small difference in
# some parameters, like the lattice constants
hamiltonian = bandcalc.calc_hamiltonian(rec_moire_lattice, potential_matrix,
mass)
k_points = bandcalc.generate_k_path(points, N)
bandstructure, prefix = bandcalc.get_unit_prefix(
bandcalc.calc_bandstructure(k_points, hamiltonian))
## Fit the Hubbard (Tight Binding) Hamiltonian
# Construct function
number_nearest_neighbours = 2
triangulation = Delaunay(moire_lattice)
zero_vec_ind = bandcalc.find_vector_index(moire_lattice, [0, 0])
nn = np.vstack([
moire_lattice[bandcalc.find_k_order_delaunay_neighbours(
zero_vec_ind,
triangulation,
k,
only_k_shell=True,
include_point_index=False)]
for k in range(1, number_nearest_neighbours + 1)
])