# Generate a real space monkhorst pack lattice
mp_moire = bandcalc.generate_monkhorst_pack_raw(m, 100)
moire_potential_pointwise = bandcalc.calc_moire_potential(mp_moire, GM, Vj)
results = {"CPU": [], "GPU": []}
########################
###### Comparison ######
########################
shells = [1, 2] #, 4, 8, 10, 12, 14, 16]
for shell in shells:
print(f"Shells: {shell}")
# Complete reciprocal moire lattice
rec_moire_lattice = bandcalc.generate_lattice_by_shell(rec_m, shell)
size = len(rec_moire_lattice)
#### CPU ####
cpu_fun = ray.remote(calc_moire_potential_reciprocal)
print("CPU calculating...")
start = time.time()
calc_potential_matrix(rec_moire_lattice, False, cpu_fun, mp_moire,
moire_potential_pointwise, False)
results["CPU"].append([size, time.time() - start])
print("Done.")
#### GPU ####
shells = args.shells
a = lattice_constants["MoS2"] * 1e9
N = 1000
mass = 0.35 * physical_constants["electron mass"][0]
# Reciprocal lattice vectors
b1 = np.array([2 * np.pi / (np.sqrt(3) * a), 2 * np.pi / a])
b2 = np.array([2 * np.pi / (np.sqrt(3) * a), -2 * np.pi / a])
b = np.vstack([b1, b2])
# Reciprocal moire basis vectors
rec_m = b - bandcalc.rotate_lattice(b, angle)
# Complete reciprocal moire lattice
rec_moire_lattice = bandcalc.generate_lattice_by_shell(rec_m, shells)
# Real space moire basis vectors
m = bandcalc.generate_reciprocal_lattice_basis(rec_m)
# Real space moire lattice vectors
moire_lattice = bandcalc.generate_lattice_by_shell(m, shells)
if potential == "MoS2":
# Moire potential coefficients
V = 6.6 * 1e-3 * np.exp(-1j * 94 * np.pi / 180) # in eV
Vj = np.array([V if i % 2 else np.conjugate(V) for i in range(1, 7)])
potential_matrix = bandcalc.calc_potential_matrix_from_coeffs(
rec_moire_lattice, Vj)
elif potential == "off":
potential_matrix = bandcalc.calc_potential_matrix(rec_moire_lattice)
import bandcalc
# Constants
a = 1
N = 1000
m_e = 0.42*bandcalc.constants.physical_constants["electron mass"][0]
m_h = 0.34*bandcalc.constants.physical_constants["electron mass"][0]
m = m_e+m_h
# Reciprocal lattice vectors
b1 = np.array([2*np.pi/a, 0, 0])
b2 = np.array([0, 2*np.pi/a, 0])
b3 = np.array([0, 0, 2*np.pi/a])
b = np.vstack([b1, b2, b3])
lattice = bandcalc.generate_lattice_by_shell(b, 2)
# k path
points = np.array([[0, 0, 0], # Gamma
[0, np.pi/a, 0], # X
[np.pi/a, np.pi/a, 0], # M
[0, 0, 0], # Gamma
[np.pi/a, np.pi/a, np.pi/a]]) # R
k_names = [r"$\Gamma$", r"X", r"M", r"$\Gamma$", r"R"]
path = bandcalc.generate_k_path(points, N)
# Calculate band structure
potential_matrix = bandcalc.calc_potential_matrix(lattice)
hamiltonian = bandcalc.calc_hamiltonian(lattice, potential_matrix, m)
bandstructure, prefix = bandcalc.get_unit_prefix(
bandcalc.calc_bandstructure(path, hamiltonian))
# Reciprocal moire lattice vectors
G = bandcalc.generate_twisted_lattice_by_shell(b, b, angle, 1)
GT = G[0]
GB = G[1]
GM = GT - GB
GM = np.array(sorted(GM, key=lambda x: np.abs(x.view(complex))))[1:]
GM = np.array(sorted(GM, key=lambda x: np.angle(x.view(complex))))
# Real space grid
size = np.linspace(-10, 10, 100)
grid = np.meshgrid(size, size)
# Results
fig, ax = plt.subplots()
moire_potential = bandcalc.calc_moire_potential_on_grid(grid, GM, Vj)
contour = bandcalc.plot_moire_potential(ax, grid, moire_potential, alpha=0.4)
twisted_lattice = bandcalc.generate_twisted_lattice_by_shell(a, a, angle, 15)
bandcalc.plot_lattice(ax, twisted_lattice[0], "r.")
bandcalc.plot_lattice(ax, twisted_lattice[1], "b.")
moire_lattice = bandcalc.generate_lattice_by_shell(m, 1)
bandcalc.plot_lattice(ax, moire_lattice, "ko")
ax.axis("scaled")
ax.set_xlim([size.min(), size.max()])
ax.set_ylim([size.min(), size.max()])
plt.colorbar(contour, label=r"$\Delta(\mathbf{r})$ in meV")
plt.show()
temperature = config["general"].getfloat("temperature")
filling = config["general"].getfloat("filling")
system_str = f"{material_system.replace('/', '_')}_{stacking}_stacking_{particle_type}"
with open(f"bandcalc/examples/hubbard/wannier_pickle/moire_vector_lengths_{system_str}.pickle", "rb") as f:
m_lens = pickle.load(f)
res = []
for angle in np.linspace(1, 3, num=10):
# Reciprocal moire basis vectors
rec_m = b1-bc.rotate_lattice(b2, angle)
# Complete reciprocal moire lattice
rec_moire_lattice = bc.generate_lattice_by_shell(rec_m, shells)
# Real space moire basis vectors
m = bc.generate_reciprocal_lattice_basis(rec_m)
# Real space moire lattice vectors
moire_lattice = bc.generate_lattice_by_shell(m, 2)
# 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)
k_points = bc.generate_monkhorst_pack_set(rec_m, 40)
## Calculate the band structure
# The bandstructure is slightly different from the bandstructure in the
mode = args.mode
a = lattice_constants["MoS2"]*1e9
N = 1000
mass = 0.35*physical_constants["electron mass"][0]
# Reciprocal lattice vectors
b1 = np.array([2*np.pi/(np.sqrt(3)*a), 2*np.pi/a])
b2 = np.array([2*np.pi/(np.sqrt(3)*a), -2*np.pi/a])
b = np.vstack([b1, b2])
# Reciprocal moire basis vectors
rec_m = b-bandcalc.rotate_lattice(b, angle)
# Complete reciprocal moire lattice
rec_moire_lattice = bandcalc.generate_lattice_by_shell(rec_m, shells)
# Real space moire basis vectors
m = bandcalc.generate_reciprocal_lattice_basis(rec_m)
if potential == "MoS2":
# Moire potential coefficients
V = 6.6*1e-3*np.exp(-1j*94*np.pi/180) # in eV
Vj = np.array([V if i%2 else np.conjugate(V) for i in range(1, 7)])
potential_matrix = bandcalc.calc_potential_matrix_from_coeffs(rec_moire_lattice, Vj)
elif potential == "off":
potential_matrix = bandcalc.calc_potential_matrix(rec_moire_lattice)
## Calculate eigenstates for every k point in the MBZ
k_points = bandcalc.generate_monkhorst_pack_set(rec_m, 20).astype(np.float32)
hamiltonian = bandcalc.calc_hamiltonian(rec_moire_lattice, potential_matrix, mass)