def demo_zigzag_lattice_oneband_uniform():
## parameter
num_layer = 2
NAPL = 4 #Number of Atoms Per Layer
NBPA = 2 #Number of Bands Per Atom
num_BF_sample = 1000
num_moment = 4
EFNN = -1 #Energy of First Nearest Neighbor
EOnsite_central = 0
EOnsite_left = 0
EOnsite_right = 0
EDisorder = 0.2
hf_rand = generate_uniform_hf_rand(-EDisorder, EDisorder)
hf_average = generate_uniform_hf_average(-EDisorder, EDisorder)
energy = np.linspace(-4, 4, 50)
energy_epsj = 1e-7j
# calculation
assert NAPL % 4 == 0
ham0 = EFNN * (np.diag(np.ones(NAPL - 1), 1) + np.diag(
np.ones(NAPL - 1), -1)) + EOnsite_left * np.eye(NAPL)
ham1 = EFNN * np.kron(
np.eye(NAPL // 4 + 1),
np.array([[0, 0, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 0, 0]
]))[:NAPL, :NAPL]
HInfo = build_device_Hamiltonian_with_ham0_ham1(ham0, ham1, num_layer)
tmp0 = [
quick_transmission_moment_BF(x + energy_epsj, HInfo, num_moment,
num_BF_sample, hf_rand)
for x in tqdm(energy)
]
T_moment_BF = np.stack(tmp0, axis=1)
matC0 = None
T_moment_FCSCPA = []
for x in tqdm(energy):
tmp0, matC0 = quick_transmission_moment_FCSCPA(x + energy_epsj,
HInfo,
num_moment,
hf_average,
matC0=matC0)
T_moment_FCSCPA.append(tmp0)
T_moment_FCSCPA = np.stack(T_moment_FCSCPA, axis=1)
## figure
# assert np.abs(T_moment_FCSCPA.imag).max() < 1e-4 #fail
tableau_colorblind = [
x['color']
for x in plt.style.library['tableau-colorblind10']['axes.prop_cycle']
]
fig, ax = plt.subplots()
for x, y, z in zip(range(num_moment), T_moment_FCSCPA.real,
tableau_colorblind):
ax.plot(energy, y, color=z, label='$tr(T^{}$)'.format(x + 1))
for x, y, z in zip(range(num_moment), T_moment_BF.real.mean(axis=2),
tableau_colorblind):
ax.plot(energy, y, 'x', color=z, markersize=2)
ax.legend()
def uniform_parameter(tag_complex=False):
N1 = np.random.randint(5, 10)
matA = np.random.randn(N1, N1) + np.eye(N1) * N1 / 2
if tag_complex:
matA = matA + (np.random.randn(N1, N1) + np.eye(N1) * N1 / 2) * 1j
x1 = np.random.rand() * 2 - 1
x2 = np.random.rand() + x1
hf_rand = generate_uniform_hf_rand(x1, x2)
hf_average = generate_uniform_hf_average(x1, x2)
return N1, matA, hf_rand, hf_average
def uniform_parameter(tag_complex=False, block_size=None):
num_block = np.random.randint(5, 10)
if block_size is None:
block_size = np.random.randint(1, 4)
else: #used for compare with CPA_general
assert isinstance(block_size, int) and block_size > 0
N1 = num_block * block_size
matA = np.random.randn(N1, N1) + np.eye(N1) * N1
matA = matA + matA.T
if tag_complex:
matA = matA + (np.random.randn(N1, N1) + np.eye(N1) * N1 / 2) * 1j
x1 = np.random.rand() * 2 - 1
x2 = np.random.rand() + x1
hf_rand = generate_uniform_hf_rand(x1, x2)
hf_average = generate_uniform_hf_average(x1, x2)
return num_block, block_size, matA, hf_rand, hf_average
def demo_square_lattice_multiband_uniform():
# parameter
num_layer = 2
NAPL = 4 #Number of Atom Per Layer
num_sample = 1000
num_moment = 4
wave_number = np.linspace(10, 900, 100) #cm-1
angular_frequency = hf_wave_numer_to_angular_frequency(
wave_number) #equivalent to Hz
energy_epsj = 1e-6j
mass_carbon = 12.0107 #in AMU
mass_left_lead = mass_carbon
mass_right_lead = mass_carbon
hf_rand = generate_uniform_hf_rand(0.9 * mass_carbon, 1.1 * mass_carbon)
hf_average = generate_uniform_hf_average(0.9 * mass_carbon,
1.1 * mass_carbon)
# Hamiltonian
ham1 = np.kron(np.eye(NAPL), hf_dynamic_matrix(30))
if NAPL > 1:
tmp1 = np.kron(np.diag(np.ones(NAPL - 1), 1), hf_dynamic_matrix(120))
ham0 = tmp1 + tmp1.T
else:
ham0 = np.zeros(3)
ham0 = build_phonon_ham0(3, ham0, ham1)
HInfo = build_device_Hamiltonian_with_ham0_ham1(ham0, ham1, num_layer)
T_moment_BF = []
for x in tqdm(angular_frequency):
hf_Bii = generate_hf_Bii(-np.ones((1, 1)) * x**2)
T_moment_BF.append(
quick_phonon_transmission_moment_BF(x, mass_left_lead,
mass_right_lead, HInfo,
num_moment, num_sample,
hf_rand, hf_Bii, energy_epsj))
T_moment_BF = np.stack(T_moment_BF, axis=1)
matC0 = None
T_moment_FCSCPA = []
for x in tqdm(angular_frequency):
hf_Bii = generate_hf_Bii(-np.ones((1, 1)) * x**2)
tmp0, matC0 = quick_phonon_transmission_moment_FCSCPA(x,
mass_left_lead,
mass_right_lead,
HInfo,
num_moment,
hf_average,
hf_Bii,
energy_epsj,
matC0=matC0)
T_moment_FCSCPA.append(tmp0)
T_moment_FCSCPA = np.stack(T_moment_FCSCPA, axis=1)
# assert np.abs(T_moment_FCSCPA.imag).max() < 1e-4
tableau_colorblind = [
x['color']
for x in plt.style.library['tableau-colorblind10']['axes.prop_cycle']
]
fig, ax = plt.subplots()
for x, y, z in zip(range(num_moment), T_moment_FCSCPA.real,
tableau_colorblind):
ax.plot(wave_number, y, color=z, label='$tr(T^{}$)'.format(x + 1))
for x, y, z in zip(range(num_moment), T_moment_BF.real.mean(axis=2),
tableau_colorblind):
ax.plot(wave_number, y, 'x', color=z, markersize=2)
ax.legend()