## Calculate eigenstates for every k point in the MBZ
k_points = bandcalc.generate_monkhorst_pack_set(rec_m, 30).astype(np.float32)
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,
moire_lattice = bc.generate_lattice_by_shell(m, shells)
# Moire potential coefficients
Vj = np.array([V if i%2 else np.conjugate(V) for i in range(1, 7)])
potential_matrix = bc.calc_potential_matrix_from_coeffs(rec_moire_lattice, Vj)
## 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]])
path = bc.generate_k_path(points, 1000)
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 = bc.calc_hamiltonian(rec_moire_lattice, potential_matrix, mass)
bandstructure = bc.calc_bandstructure(path, hamiltonian)
## Fit the Hubbard (Tight Binding) Hamiltonian
# Construct function
number_nearest_neighbours = 2
triangulation = Delaunay(moire_lattice)
zero_vec_ind = bc.find_vector_index(moire_lattice, [0, 0])
nn = np.vstack([moire_lattice[bc.find_k_order_delaunay_neighbours(zero_vec_ind, triangulation, k,