def main():
# Define the system
parameters = gasb.params_97
hamiltonian = gasb.hamiltonian_97_k_plus()
Width = shapes.W_STD
a_lattice = shapes.A_STD
syst_inf = gasb.just_lead_builder(hamiltonian,
Width,
a_lattice,
symmetry=1)
# Calculate the energies at kx == 0
min_field = 0
max_field = 5000
N_pts = 5001
efield_values = np.linspace(min_field, max_field, N_pts)
energies_conf = trans.collected_energies(syst_inf, parameters,
efield_values)
energies_free = trans.continuous_levels_eF(0, 0, hamiltonian, parameters,
efield_values)
# Save the results
path_data = './data/band_structure/'
name = '97_landau_levels_' + 'eF_min_' + str(min_field) + \
'_max_' + str(max_field) + '_N_' + str(N_pts)
np.savez(path_data + name,
efields=efield_values,
Energies_conf=energies_conf,
Energies_free=energies_free)
# Plot the results
"Formatação para os gráficos:"
FONT_LABELS = 18
FONT_TITLES = 20
font = {'family': 'serif', 'weight': 'bold', 'size': FONT_LABELS}
matplotlib.rc('font', **font)
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
"Actual plot:"
fig, ax = plt.subplots(figsize=(7, 8))
ax.plot(efield_values,
energies_conf,
color='k',
linestyle='',
marker=',',
linewidth=0.7)
ax.plot(efield_values, energies_free, color='b', linewidth=2)
ax.set_xlabel(r'eF [meV]', fontsize=FONT_TITLES)
ax.set_ylabel(r'$\varepsilon$ [meV]', fontsize=FONT_TITLES)
# ax.set_ylim(410, 550)
ax.set_xlim(min_field, max_field)
plt.tight_layout()
plt.show()
def main():
## Dimensions of the system:
Length = shapes.W_STD
Width = shapes.W_STD
shapeScattering = shapes.Rect(Width, Length)
params_raw = gasb.params_97
gammaLead = 36.917
V_shift = 100
params_dict = dict(GammaLead=gammaLead, V=V_shift, **params_raw)
hamiltonian_syst = gasb.hamiltonian_97_k_plus()
hamiltonian_lead = gasb.free_ham(norbs=6)
sistema = gasb.system_builder(hamiltonian_syst, hamiltonian_lead,
shapeScattering)
# sistema_dn = gasb.system_builder(hamiltonian_syst_dn, hamiltonian_lead, shapeScattering)
Fermi_initial, Fermi_final, N_values = 435, 440, 2001
Fermi_values = np.linspace(Fermi_initial, Fermi_final, N_values)
params_dict['eF'] = 62.
## " Names for the files: "
L_nm = Length * shapes.A0 * 1 / 10
path_data = "./data/transport/"
name_preffixe = "data_" + str(Fermi_initial) + "_" + str(
Fermi_final) + "_meV_Fermi_"
name_Fermi = name_preffixe + str(N_values) + "_L_" + str(L_nm)
name_transport_up = name_preffixe + "Transport_UP_" + str(
N_values) + "_L_" + str(L_nm)
name_transport_dn = name_preffixe + "Transport_DN_" + str(
N_values) + "_L_" + str(L_nm)
name_transport_total = name_preffixe + "Transport_Total_" + str(
N_values) + "_L_" + str(L_nm)
np.save(path_data + name_Fermi + ".npy", Fermi_values)
np.savetxt(path_data + name_Fermi + ".txt", Fermi_values)
## " Transport: "
transport_up, transport_dn, transport_total = calc_transp_Fermi(
sistema, Fermi_values, params_dict)
# Save the results in "numpy" format and "txt"
# np.save(path_data + name_transport_up + ".npy", transport_up)
# np.savetxt(path_data + name_transport_up + ".txt", transport_up)
#
# np.save(path_data + name_transport_dn + ".npy", transport_dn)
# np.savetxt(path_data + name_transport_dn + ".txt", transport_dn)
np.save(path_data + name_transport_total + ".npy", transport_total)
np.savetxt(path_data + name_transport_total + ".txt", transport_total)
def main():
"""
This code is for generate maps of current, without bands structures and
with custom operators. This will allow a better exploratory process.
"""
# Define the system
hamiltonian = gasb.hamiltonian_97_k_plus()
lead_ham = gasb.free_ham(norbs = 6)
centralShape = shapes.Rect(Wmax = 300, Lmax=500)
syst = gasb.system_builder(hamiltonian, lead_ham, centralShape, a_lattice=20)
fig, axis = plt.subplots(1,1,figsize=(10,5))
kwant.plot(syst, ax = axis, show = False)
axis.axis('off')
axis.set_aspect('equal')
plt.show()
def main():
# Define the system
raio_simples = 10 * shapes.A_STD
# raio_nm = 150
# raio_std = raio_nm * 10/shapes.A0
print("QD radius: ", raio_simples, " Bohr radia.")
# lattice_const_Bohr_radia = 200
lattice_const_Bohr_radia = shapes.A_STD
formato = shapes.Circular(raio_simples)
H = gasb.hamiltonian_97_k_plus()
quantum_dot = gasb.just_system_builder(H,
formato,
a_lattice=lattice_const_Bohr_radia)
# Check that the system looks as intended.
kwant.plot(quantum_dot)
# Define parameters
min_field = 0
max_field = 1000
N_pts = 1000
eF_values = np.linspace(min_field, max_field, N_pts)
parametros = gasb.params_97
# Calculate and save energy levels of the dot
energies = calc_spectrum(quantum_dot, eF_values, parametros)
np.savez(
"circular_quantum_dot_energies_around_445_meV_field_0_62_and_200_eigenstates_R_150nm_a_200A0.npz",
Ef_values=eF_values,
Energies=energies)
# and plot the results
plt.figure()
plt.plot(eF_values, energies, linestyle=' ', marker=',', color='k')
plt.xlabel("E. field [meV]")
plt.ylabel(r"$\varepsilon$ [meV]")
plt.tight_layout()
plt.show()
def main():
"""
This code is for generate maps of current, without bands structures and
with custom operators. This will allow a better exploratory process.
"""
# Define the system
hamiltonian = gasb.hamiltonian_97_k_plus()
lead_ham = gasb.free_ham(norbs = 6)
centralShape = shapes.Rect()
syst = gasb.system_builder(hamiltonian, lead_ham, centralShape)
# Calculate the wave function:
energia = 442
parametros = gasb.params_97
parametros['eF'] = 60
parametros['Eta2'] = 0
parametros['Eta3'] = 0
parametros = dict(GammaLead = parametros["GammaC"], V = 100, **parametros)
wf = kwant.wave_function(syst, energy=energia, params=parametros)
# modes = wf_dn(0) # from left lead
# Define the operator
σz = tinyarray.array([[1,0],[0,-1]])
Mz = np.kron(σz, np.eye(3))
# Current
colormap = "Reds"
J_spin = kwant.operator.Current(syst, Mz)
current_spin = sum(J_spin(psi, params = parametros) for psi in wf(0))
# Plot and/or save the data
fig, axis = plt.subplots(1,1, figsize=(8,8))
kwant.plotter.current(syst, current_spin,
cmap = colormap,
colorbar = False,
show = False,
ax = axis)
edit_axis(axis)
plt.show()
def main():
shapeScattering = shapes.Rect(shapes.W_STD, shapes.L_STD)
params_raw = gasb.params_97
gammaLead = 36.917
V_shift = 100
params_dict = dict(GammaLead=gammaLead, V=V_shift, **params_raw)
hamiltonian_syst = gasb.hamiltonian_97_k_plus()
hamiltonian_lead = gasb.free_ham(norbs=6)
sistema = gasb.system_builder(hamiltonian_syst, hamiltonian_lead,
shapeScattering)
eF_initial, eF_final, N_values = 62, 64, 501
eF_values = np.linspace(eF_initial, eF_final, N_values)
"Transport: "
energy = 440
transport = np.empty(len(eF_values))
for i in range(len(eF_values)):
params_dict['eF'] = eF_values[i]
# compute the scattering matrix at a given energy
smatrix = kwant.smatrix(sistema, energy, params=params_dict)
# compute the transmission probability from lead 0 to lead 1
transport[i] = smatrix.transmission(1, 0)
path_data = "./data/transport/"
name_preffixe = "data_" + str(eF_initial) + "_" + str(eF_final) + "_"
name_eF = name_preffixe + "eF_" + str(N_values)
name_transport = name_preffixe + "Transport_" + str(N_values)
np.save(path_data + name_eF + ".npy", eF_values)
np.savetxt(path_data + name_eF + ".txt", eF_values)
np.save(path_data + name_transport + ".npy", transport)
np.savetxt(path_data + name_transport + ".txt", transport)
def main():
# Define Hamiltonians
hamiltonian = gasb.hamiltonian_97_k_plus()
# Define the system
symm_dir = 1 # symmetry direction
syst_lead_up = gasb.just_lead_builder(hamiltonian, symmetry=symm_dir)
# Set params
eF0 = 0
eF1 = 20
eF2 = 60
parametros = gasb.params_97
# Define momentum array
Nkx = 200
porcent = 0.15
momenta = np.linspace(-1, 1, Nkx) * np.pi * porcent
# Define bands
parametros["eF"] = eF0
bands_left = kwant.physics.Bands(syst_lead_up, params=parametros)
parametros["eF"] = eF1
bands_center = kwant.physics.Bands(syst_lead_up, params=parametros)
parametros["eF"] = eF2
bands_right = kwant.physics.Bands(syst_lead_up, params=parametros)
# Calculate Bands for the stripped system
energies_left = [bands_left(k) for k in momenta]
energies_center = [bands_center(k) for k in momenta]
energies_right = [bands_right(k) for k in momenta]
# Calculate the Bands for the bulk system
bulk_left = tools.continuous_bands_2D(momenta / shapes.A_STD,
0,
hamiltonian,
parametros,
eF_value=eF0)
bulk_center = tools.continuous_bands_2D(momenta / shapes.A_STD,
0,
hamiltonian,
parametros,
eF_value=eF1)
bulk_right = tools.continuous_bands_2D(momenta / shapes.A_STD,
0,
hamiltonian,
parametros,
eF_value=eF2)
# Plot bands for strip
E_min_plot = 420
E_max_plot = 460
max_kx = 0.15
fig, ax = plt.subplots(1, 3, figsize=(14, 7))
tools.band_with_line_gasb(ax[0],
momenta,
energies_left,
kx_max=max_kx,
E_max=E_max_plot,
E_min=E_min_plot)
tools.band_with_line_gasb(ax[1],
momenta,
energies_center,
kx_max=max_kx,
E_max=E_max_plot,
E_min=E_min_plot)
tools.band_with_line_gasb(ax[2],
momenta,
energies_right,
kx_max=max_kx,
E_max=E_max_plot,
E_min=E_min_plot)
# Plot bands for bulk
momenta_bulk = tools.trans_momenta(momenta)
ax[0].plot(momenta_bulk, bulk_left, linewidth=1.5, color="red")
ax[0].set_title("x = %.1f meV" % eF0)
ax[1].plot(momenta_bulk, bulk_center, linewidth=1.5, color="red")
ax[1].set_title("x = %.1f meV" % eF1)
ax[2].plot(momenta_bulk, bulk_right, linewidth=1.5, color="red")
ax[2].set_title("x = %.1f meV" % eF2)
plt.tight_layout()
plt.show()
def main():
# Define Hamiltonians
ham_up = gasb.hamiltonian_97_up()
ham_dn = gasb.hamiltonian_97_down()
ham_total = gasb.hamiltonian_97_k_plus()
# Define the system
symm_dir = 1 # symmetry direction
syst_lead_up = gasb.just_lead_builder(ham_up, symmetry = symm_dir)
syst_lead_dn = gasb.just_lead_builder(ham_dn, symmetry = symm_dir)
syst_total = gasb.just_lead_builder(ham_total)
# Set params
eF = 60
parametros = gasb.params_97
parametros["eF"] = eF
# Define momentum array
Nkx = 200
porcent = 0.15
momenta = np.linspace(-1, 1, Nkx) * np.pi * porcent
# Define bands
bands_coupled = kwant.physics.Bands(syst_total, params = parametros)
bands_up = kwant.physics.Bands(syst_lead_up, params = parametros)
bands_dn = kwant.physics.Bands(syst_lead_dn, params = parametros)
# Calculate Bands for the stripped system
energies_up = [bands_up(k) for k in momenta]
energies_dn = [bands_dn(k) for k in momenta]
energies_coupled = [bands_coupled(k) for k in momenta]
# Calculate the Bands for the bulk system
bulk_up = tools.continuous_bands_2D(momenta/shapes.A_STD, 0, ham_up, parametros, eF_value = eF)
bulk_dn = tools.continuous_bands_2D(momenta/shapes.A_STD, 0, ham_dn, parametros, eF_value = eF)
bulk_total = tools.continuous_bands_2D(momenta/shapes.A_STD, 0, ham_total,parametros, eF_value = eF)
# Plot bands for strip
E_min_plot = 420
E_max_plot = 460
fig, ax = plt.subplots(1, 3, figsize=(14,7))
tools.band_with_line_gasb(ax[0], momenta, energies_up,
kx_max = 0.15, E_max = E_max_plot, E_min = E_min_plot)
tools.band_with_line_gasb(ax[1], momenta, energies_dn,
kx_max = 0.15, E_max = E_max_plot, E_min = E_min_plot)
tools.band_with_line_gasb(ax[2], momenta, energies_up,
kx_max = 0.15, E_max = E_max_plot, E_min = E_min_plot,
linestyle_plot = "-", color_plot = "black",
label_plot = "Up")
tools.band_with_line_gasb(ax[2], momenta, energies_dn,
kx_max = 0.15, E_max = E_max_plot, E_min = E_min_plot,
linestyle_plot = "--", color_plot = "black",
label_plot = "Down")
# tools.band_with_line_gasb(ax[2], momenta, energies_coupled,
# kx_max = 0.15, E_max = E_max_plot, E_min = E_min_plot,
# linestyle_plot = "--", color_plot = "black",
# marker_plot = None, label_plot = "Coupled")
# Plot bands for bulk
momenta_bulk = tools.trans_momenta(momenta)
ax[0].plot(momenta_bulk, bulk_up, linewidth=2.5, color="red")
# ax[1].plot([0.03733],[440],marker = "o", markersize = 7, color = "blue")
ax[0].set_title("(a)")
ax[1].plot(momenta_bulk, bulk_dn, linewidth=2.5, color="blue")
# ax[0].plot([0.02784],[440], marker = "o", markersize = 7, color = "red")
ax[1].set_title("(b)")
ax[2].set_title("(c)")
ax[2].plot(momenta_bulk, bulk_up, linewidth=2.5, color="red")
ax[2].plot(momenta_bulk, bulk_dn, linewidth=2.5, color="blue")
ax[2].legend(fontsize = 13, bbox_to_anchor = (0.64, 0.7))
plt.tight_layout()
plt.show()
def main():
# Define the system:
hamiltonian = gasb.hamiltonian_97_k_plus()
# hamiltonian = gasb.hamiltonian_97_down()
lead_ham = gasb.free_ham(6)
centralShape = shapes.Rect()
syst = gasb.system_builder(hamiltonian, lead_ham, centralShape)
# Calculate the wave_function:
energia = 448
parametros = gasb.params_97
parametros['Eta3'] = 0
parametros['Eta2'] = 0
parametros['eF'] = 60
parametros = dict(GammaLead = parametros["GammaC"], V = 100, **parametros )
wf = kwant.wave_function(syst, energy = energia, params = parametros)
modes_left = wf(0)
modes_right = wf(1)
# modes_total = np.vstack((wf(0), wf(1)))
# Calculate the density:
sigma_z = tinyarray.array([[1,0],[0,-1]])
spin_proj= np.kron(sigma_z, np.eye(3))
identity = np.eye(6)
rho = kwant.operator.Density(syst, spin_proj)
psi_left = sum(rho(p) for p in modes_left)
psi_right = sum(rho(p) for p in modes_right)
# Calculate dos in a line
dos_in_line_from_left = density_in_line(syst, psi)
dos_in_line_from_both = density_in_line(syst, np.vstack((wf(0),wf(1))))
plt.plot(sum(dos_in_line_from_both))
plt.show()
# print(dos_in_line.shape)
# print(dos_in_line)
plot_dos_in_line(dos_in_line_from_left)
# plot_dos_in_line(dos_in_line_from_both)
print(sum(dos_in_line_from_both).shape)
# Plot the results:
colorRight = "seismic"
colorLeft = "seismic"
fig, ax = plt.subplots(2,2,figsize=(14,6))
y_values_left = y_values_left * (shapes.A0 / 10) # conversion to nm^{-1}
y_values_right = y_values_right * (shapes.A0 / 10) # conversion to nm^{-1}
min_line, max_line = -0.7 * shapes.L_STD, 0.7 * shapes.L_STD
map_density(ax[0][0], syst, psi_left, colormap = colorRight)
ax[0][0].vlines(0, min_line, max_line, linestyle = "--")
ax[0][0].set_title("left lead")
map_density(ax[1][0], syst, psi_right, colormap = colorLeft)
ax[1][0].vlines(0, min_line, max_line, linestyle = "--")
ax[1][0].set_title("right lead")
ax[0][1].plot(y_values_left, normalize(dos_in_line_from_left),
marker = ".", markersize = 2.5, linestyle = "-" )
ax[1][1].plot(y_values_right, normalize(dos_in_line_from_right),
marker = ".", markersize = 2.5, linestyle = "-" )
plt.tight_layout()
plt.show()