def test_uniform_compare_with_CPA_general():
num_block, block_size, matA, _, hf_average = uniform_parameter(
block_size=1)
matC_ = CPA_general(matA, hf_average)
hf_Bii = generate_hf_Bii(np.ones((1, 1)))
matC = CPA_block_general(matA, block_size, hf_Bii, hf_average)[:, 0, 0]
assert hfe(matC_, matC) < 1e-7, f'num_block={num_block}'
def test_binary_compare_with_CPA_general():
num_block, block_size, matA, _, hf_average = binary_parameter(block_size=1)
matC_ = CPA_general(matA, hf_average)
hf_Bii = generate_hf_Bii(np.ones((1, 1)))
matC = CPA_block_general(matA, block_size, hf_Bii, hf_average)[:, 0, 0]
tmp1 = hfe(matC_, matC)
assert tmp1 < 1e-7, f'num_block={num_block}'
def demo_square_lattice_multiband_binary():
## parameter
num_layer = 2
NAPL = 4 #Number of Atoms Per Layer
NBPA = 2 #Number of Bands Per Atom
num_BF_sample = 100
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_binary_hf_rand(-EDisorder, 0.5, EDisorder)
hf_average = generate_binary_hf_average(-EDisorder, 0.5, EDisorder)
hf_Bii = generate_hf_Bii(np.array([[0, 1], [1, 0]]))
energy = np.linspace(-4, 4, 50)
energy_epsj = 1e-7j
# calculation
ham0 = EFNN * (np.diag(np.ones(NAPL - 1), 1) + np.diag(
np.ones(NAPL - 1), -1)) + EOnsite_left * np.eye(NAPL)
ham0 = np.kron(ham0, np.eye(NBPA))
ham1 = EFNN * np.eye(NBPA * 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, hf_Bii)
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,
hf_Bii=hf_Bii,
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 sometimes
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 test_uniform_real():
num_block, block_size, matA, hf_rand, hf_average = uniform_parameter(
tag_complex=False)
hf_Bii = generate_hf_Bii(np.random.randn(block_size, block_size))
N2 = 10000
hf1 = lambda: Aii_to_matA(hf_Bii(hf_rand(num_block)).transpose(2, 0, 1))
ret1 = sum(np.linalg.inv(matA - hf1()) for _ in range(N2)) / N2
ret2 = sum(np.linalg.inv(matA - hf1()) for _ in range(N2)) / N2
matC = CPA_block_general(matA,
block_size,
hf_Bii,
hf_average,
tag_complex=False)
ret3 = np.linalg.inv(matA - Aii_to_matA(matC))
tmp1 = hfe(ret1, ret2)
tmp2 = hfe((ret1 + ret2) / 2, ret3)
assert tmp2 < tmp1 * 2, f'num_block={num_block}, block_size={block_size}'
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()
def demo_zigzag_lattice_multiband_binary():
# parameter
num_layer = 2
NAPL = 4 #Number of Atom Per Layer
num_sample = 1000
num_moment = 4
wave_number = np.linspace(10, 1600, 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_binary_hf_rand(0.9 * mass_carbon, 0.5,
1.1 * mass_carbon)
hf_average = generate_binary_hf_average(0.9 * mass_carbon, 0.5,
1.1 * mass_carbon)
# Hamiltonian
hf1 = lambda x: slice(3 * x, 3 * x + 3)
ham1 = np.zeros([3 * NAPL, 3 * NAPL])
for ind1, x in zip(range(NAPL),
itertools.cycle([None, (-1, -30), (1, 30), None])):
if x is not None:
ham1[hf1(ind1), hf1(ind1 + x[0])] = hf_dynamic_matrix(x[1])
ham0 = np.zeros([3 * NAPL, 3 * NAPL])
for ind1, theta in enumerate(
np.tile(np.array([30, 90, 150, 90]),
[NAPL // 4 + 1])[:(NAPL - 1)]):
ham0[hf1(ind1), hf1(ind1 + 1)] = hf_dynamic_matrix(theta)
ham0 = build_phonon_ham0(3, ham0 + ham0.T, 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()
def demo_square_lattice_oneband_binary():
# parameter
num_layer = 20
NAPL = 20 #Number of Atom Per Layer
num_sample = 1000
num_moment = 4
wave_number = np.linspace(10, 1700, 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_binary_hf_rand(0.9 * mass_carbon, 0.5,
1.1 * mass_carbon)
hf_average = generate_binary_hf_average(0.9 * mass_carbon, 0.5,
1.1 * mass_carbon)
# Hamiltonian
force_constant = -FORCE_CONSTANT_Dresselhaus[
0, 0] #see RGF.phonon_utils.FORCE_CONSTANT_Dresselhaus
ham1 = np.ones((1, 1)) * force_constant
ham0 = np.ones((1, 1)) * (-2 * force_constant)
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)
# use previous matC0 doesn't make any help
# 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()
hf_fL = generate_distribution_function(temperature_left)
fL = hf_fL(angular_frequency)
temperature_right = 295 #Kelvin
hf_fR = generate_distribution_function(temperature_right)
fR = hf_fR(angular_frequency)
linear_factor = linear_factor_with_hw_one(temperature_left, temperature_right, wave_number)
cumulant_coeff = []
for n in range(1, num_cumulant+1):
tmp1 = []
for m in range(1, n+1):
matA,matB = Ymn_Leibniz_matAB(m, n)
tmp1.append(Ymn_Leibniz(fL, fR, matA, matB, 'phonon') * (-1/(2*m)))
cumulant_coeff.append(np.array(tmp1))
hf_Bii = generate_hf_Bii(-angular_frequency**2*np.eye(3))
disorder_strength = np.linspace(0.01, 0.5) #large disorder will case large image part
mass_disorder = [((1-x)*mass_carbon, 0.5, (1+x)*mass_carbon) for x in disorder_strength]
## 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)
## parameter
num_layer = 2
NAPL = 4 #Number of Atoms Per Layer
num_cumulant = 8 #the cumulant_coeff will diverge for num_cumulant>=10 (2147483647)
EFNN = -2.6 #Energy of First Nearest Neighbor
EOnsite_central = 0
EOnsite_left = 0
EOnsite_right = 0
chemical_potential_left = 0.5003
chemical_potential_right = 0.4997
temperature = 100 #kelvin
EDisorder = np.linspace(0.01, 1)
# hf_average = generate_binary_hf_average(-EDisorder, 0.5, EDisorder)
hf_Bii = generate_hf_Bii(np.array([[0, 1], [1, 0]]))
energy = 0.5
energy_epsj = 1e-7j
fL = hf_distribution_function(temperature, energy, chemical_potential_left)
fR = hf_distribution_function(temperature, energy, chemical_potential_right)
linear_factor = linear_factor_small_potential_difference_limit(
chemical_potential_left, chemical_potential_right, temperature)
# Ymn_matAB = [[Ymn_Leibniz_matAB(m,n) for m in range(1,n+1)] for n in range(1, num_cumulant+1)]
cumulant_coeff = []
for n in range(1, num_cumulant + 1):
tmp1 = []
for m in range(1, n + 1):
matA, matB = Ymn_Leibniz_matAB(m, n)
tmp1.append(
