def main():
# Define the system:
hamiltonian_up = gasb.hamiltonian_97_up()
hamiltonian_dn = gasb.hamiltonian_97_up_y_inv()
lead_ham = gasb.hamiltonian_97_up(-100)
centralShape = shapes.Rect()
syst_up = gasb.system_builder(hamiltonian_up, lead_ham, centralShape)
syst_dn = gasb.system_builder(hamiltonian_dn, lead_ham, centralShape)
# Calculate the wave_function:
energia = 442
parametros = gasb.params_97
parametros['eF'] = 60
# parametros = dict(GammaLead = parametros["GammaC"], V = 100, **parametros )
wf_up = kwant.wave_function(syst_up, energy=energia, params=parametros)
wf_dn = kwant.wave_function(syst_dn, energy=energia, params=parametros)
modes_up = wf_up(0) # from left lead
modes_dn = wf_dn(0) # from left lead
# Calculate the density:
rho_up = kwant.operator.Density(syst_up)
rho_dn = kwant.operator.Density(syst_dn)
psi_up = sum(rho_up(p) for p in modes_up)
psi_dn = sum(rho_dn(p) for p in modes_dn)
# Calculate dos in a line
dos_in_line_up, y_values_up = density_in_line(syst_up, modes_up)
dos_in_line_dn, y_values_dn = density_in_line(syst_dn, modes_dn)
# Plot the results:
fig, ax = plt.subplots(2, 2, figsize=(14, 6))
y_values_up = y_values_up * (shapes.A0 / 10) # conversion to nm^{-1}
y_values_dn = y_values_dn * (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_up, psi_up, colormap="Reds")
ax[0][0].vlines(0, min_line, max_line, linestyle="--")
ax[0][0].set_title("spin up")
map_density(ax[1][0], syst_dn, psi_dn, colormap="Blues")
ax[1][0].vlines(0, min_line, max_line, linestyle="--")
ax[1][0].set_title("spin up inv.")
ax[0][1].plot(y_values_up,
normalize(dos_in_line_up),
marker=".",
markersize=2.5,
linestyle="-",
color="red")
ax[1][1].plot(y_values_dn,
normalize(dos_in_line_dn),
marker=".",
markersize=2.5,
linestyle="-")
plt.tight_layout()
plt.show()
def test_density_interpolation():
## Passing a Builder will raise an error
pytest.raises(TypeError, plotter.interpolate_density, syst_2d(), None)
# Test that the density is always identically zero at the box boundaries
# as the bump function has finite support and we add a padding
_test_border_0(kwant.plotter.interpolate_density)
def R(theta):
return ta.array([[cos(theta), -sin(theta)], [sin(theta), cos(theta)]])
# Make lattice with lattice vectors perturbed from x and y directions
def make_lattice(a, salt='0'):
theta_x = kwant.digest.uniform('x', salt=salt) * np.pi / 6
theta_y = kwant.digest.uniform('y', salt=salt) * np.pi / 6
x = ta.dot(R(theta_x), (a, 0))
y = ta.dot(R(theta_y), (0, a))
return kwant.lattice.general([x, y], norbs=1)
# Check that integrating the interpolated density gives the same result
# as summing the densities on all sites. We check this for several lattice
# widths, lattice orientations and bump widths.
for a, width in itertools.product((1, 2), (1, 0.5)):
lat = make_lattice(a)
syst = syst_rect(lat, salt='0').finalized()
psi = kwant.wave_function(syst, energy=3)(0)[0]
density = kwant.operator.Density(syst)(psi)
exact_charge = sum(density)
# We verify that the result is good by interpolating for
# various numbers of points-per-bump and verifying that
# the error falls of as 1/n.
data = []
for n in [4, 6, 8, 11, 16]:
rho, box = plotter.interpolate_density(syst,
density,
n=n,
abswidth=width)
(xmin, xmax), (ymin, ymax) = box
area = xmax - xmin * (ymax - ymin)
N = rho.shape[0] * rho.shape[1]
charge = np.sum(rho) * area / N
data.append((n, abs(charge - exact_charge)))
_, _, rvalue, *_ = scipy.stats.linregress(np.log(data))
# Gradient of -1 on log-log plot means error falls off as 1/n
# TODO: review this value once #280 has been dealt with.
assert rvalue < -0.7
# Test that the interpolation is linear in the input.
rng = ensure_rng(1)
lat = make_lattice(1, '1')
syst = syst_rect(lat, salt='1').finalized()
rho_0 = rng.rand(len(syst.sites))
rho_1 = rng.rand(len(syst.sites))
irho_0, _ = plotter.interpolate_density(syst, rho_0)
irho_1, _ = plotter.interpolate_density(syst, rho_1)
rho_tot, _ = plotter.interpolate_density(syst, rho_0 + 2 * rho_1)
assert np.allclose(rho_tot, irho_0 + 2 * irho_1)
def test_opservables_spin():
def onsite(site, B):
return 2 * np.eye(2) + B * sigmaz
L = 20
lat = kwant.lattice.chain(norbs=2)
syst = kwant.Builder()
syst[(lat(i) for i in range(L))] = onsite
syst[lat.neighbors()] = -1 * np.eye(2)
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, )))
lead[lat(0)] = onsite
lead[lat.neighbors()] = -1 * np.eye(2)
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
args = (0.1, )
down, up = kwant.wave_function(fsyst, energy=1., args=args)(0)
x_hoppings = kwant.builder.HoppingKind((1, ), lat)
spin_current_z = ops.Current(fsyst, sigmaz, where=x_hoppings(syst))
_test(spin_current_z, up, args=args, per_el_val=1)
_test(spin_current_z, down, args=args, per_el_val=-1)
# calculate spin_x torque
spin_torque_x = ops.Source(fsyst, sigmax, where=[lat(L // 2)])
i = fsyst.id_by_site[lat(L // 2)]
psi = up[2 * i:2 * (i + 1)] + down[2 * i:2 * (i + 1)]
H_ii = onsite(None, *args)
K = np.dot(H_ii, sigmax) - np.dot(sigmax, H_ii)
expect = 1j * ft.reduce(np.dot, (psi.conj(), K, psi))
_test(spin_torque_x, up + down, args=args, reduced_val=expect)
def dwell(cishu):
e1=ens[cishu]
tt = dg.t_gf(sys,e1,df)
wf=kwant.wave_function(sys,e1)(0)[0]
wf_integral=sum(abs(wf)**2)/2/np.pi
return [tt,wf_integral]
def wf_integral_all(sys, e1):
wf = kwant.wave_function(sys, e1)
wf0 = wf(0)[0]
wf1 = wf(1)[0]
return np.array(
[sum(abs(wf0)**2) / 2 / np.pi,
sum(abs(wf1)**2) / 2 / np.pi])
def main():
for i in [150,300,400,500,600,800,1000,1500]:
print('----------------------------------------')
sys_size=i
start_time = time.time()
syst = make_system(sys_size).finalized()
print("------- system creation: %s seconds ---" % (time.time() - start_time))
params = dict(r0=20, delta=10, J=1)
start_time = time.time()
wf = kwant.wave_function(syst, energy=-1, params=params)
print("------- wave functions calculation: %s seconds ---" % (time.time() - start_time))
psi = wf(0)[0]
size = (syst.cell_size if isinstance(syst, kwant.system.InfiniteSystem) else syst.graph.num_nodes)
# print(size*2, " ", (time.time() - start_time), file=open("sys_creat-times-OpStrings.dat", "a"))
psi = np.zeros(size*2, dtype=complex)
start_time = time.time()
offECurr = generalOperator.offEnergyCurrentLead(syst, where=[None,None])
# offECurr = generalOperatorStringsNotCalledNoPrints.offEnergyCurrentLead(syst, where=[None,None])
print("------- operator initialisation: %s seconds ---" % (time.time() - start_time))
# print(size*2, " ", (time.time() - start_time), file=open("init-times-OpStrings.dat", "a"))
# # calculate the expectation values of the operators with 'psi'
start_time = time.time()
ecurr = offECurr(psi)
print("------- operator calculation: %s seconds ---" % (time.time() - start_time))
# print(size*2, " ", (time.time() - start_time), file=open("call-times-OpStrings.dat", "a"))
print(ecurr)
def test_opservables_scattering():
# Disordered system with two ordered strips on the left/right. We check
# that the current on the right of the disorder due to incoming mode `m` is
# equal to Σ_n |t_nm|^2. Similarly the current on the left of the disorder
# is checked against 1 - Σ_n |r_nm|^2
N = 10
lat, syst = _random_square_system(N)
# add extra sites so we can calculate the current in a region
# where there is no backscattering
syst[(lat(i, j) for i in [-1, N] for j in range(N))] = 2
syst[((lat(-1, j), lat(0, j)) for j in range(N))] = -1
syst[((lat(N-1, j), lat(N, j)) for j in range(N))] = -1
lat, lead = _perfect_lead(3)
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
# currents on the left and right of the disordered region
J_right = ops.Current(fsyst, where=[(lat(N, j), lat(N-1, j))
for j in range(3)])
J_left = ops.Current(fsyst, where=[(lat(0, j), lat(-1, j))
for j in range(3)])
smatrix = kwant.smatrix(fsyst, energy=1.0)
t = smatrix.submatrix(1, 0).T # want to iterate over the columns
r = smatrix.submatrix(0, 0).T # want to iterate over the columns
wfs = kwant.wave_function(fsyst, energy=1.0)(0)
for rv, tv, wf in zip(r, t, wfs):
_test(J_right, wf, reduced_val=np.sum(np.abs(tv)**2))
_test(J_left, wf, reduced_val=(1 - np.sum(np.abs(rv)**2)))
def test_opservables_spin():
def onsite(site, B):
return 2 * np.eye(2) + B * sigmaz
L = 20
lat = kwant.lattice.chain(norbs=2)
syst = kwant.Builder()
syst[(lat(i) for i in range(L))] = onsite
syst[lat.neighbors()] = -1 * np.eye(2)
lead = kwant.Builder(kwant.TranslationalSymmetry((-1,)))
lead[lat(0)] = onsite
lead[lat.neighbors()] = -1 * np.eye(2)
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
args = (0.1,)
down, up = kwant.wave_function(fsyst, energy=1., args=args)(0)
x_hoppings = kwant.builder.HoppingKind((1,), lat)
spin_current_z = ops.Current(fsyst, sigmaz, where=x_hoppings(syst))
_test(spin_current_z, up, args=args, per_el_val=1)
_test(spin_current_z, down, args=args, per_el_val=-1)
# calculate spin_x torque
spin_torque_x = ops.Source(fsyst, sigmax, where=[lat(L//2)])
i = fsyst.id_by_site[lat(L//2)]
psi = up[2*i:2*(i+1)] + down[2*i:2*(i+1)]
H_ii = onsite(None, *args)
K = np.dot(H_ii, sigmax) - np.dot(sigmax, H_ii)
expect = 1j * ft.reduce(np.dot, (psi.conj(), K, psi))
_test(spin_torque_x, up+down, args=args, reduced_val=expect)
def wf_01(cishu):
en=en_wf[cishu]
wf=kwant.wave_function(sys,en)(0)[0]
# gf=kwant.greens_function(sys,en).submatrix(1,0)[:,0]
myDict = {'wf':wf}
completeName = os.path.join('E:/dwell3/786/', str(cishu)+".mat")
sio.savemat(completeName,myDict,oned_as='row')
def current_density(axis,
syst,
parameters,
eF_value=0,
energy=428,
lead_index=0,
colormap="Reds"):
parameters["eF"] = eF_value
wf = kwant.wave_function(syst, energy=energy, params=parameters)
J_spin = kwant.operator.Current(syst)
current_spin = sum(
J_spin(psi, params=parameters) for psi in wf(lead_index))
# kwant.plotter.current(syst, current_spin, cmap = colormap, colorbar = False, show = False, ax=axis, density=1/9)
kwant.plotter.current(syst,
current_spin,
cmap=colormap,
colorbar=False,
show=False,
ax=axis)
edit_axis(axis, "none") # change units to nm
axis.set_title(" ")
return 0
def test_opservables_gauged():
# Test that we get the same answer when we apply a random
# gauge (unitary) transformation to each site. We also
# adjust our definition of the current to match
# this is to get round a bug in test_mask_interpolate (?!) that fails when
# the random number state is altered.
@contextmanager
def save_random_state():
old_state = np.random.get_state()
yield
np.random.set_state(old_state)
L = 20
with save_random_state():
Us = deque([kwant.rmt.circular(2) for i in range(L)])
# need these to get the coupling to the leads right
Us.append(np.eye(2))
Us.appendleft(np.eye(2))
H0 = 2 * np.eye(2) + 0.1 * sigmaz # onsite
V0 = -1 * np.eye(2) # hopping
lat = kwant.lattice.chain(norbs=2)
syst = kwant.Builder()
for i, U in enumerate(Us):
syst[lat(i)] = ft.reduce(np.dot, (U, H0, U.conjugate().transpose()))
for a, b in kwant.builder.HoppingKind((1, ), lat)(syst):
i, j = a.tag[0], b.tag[0]
syst[(a, b)] = ft.reduce(np.dot,
(Us[i], V0, Us[j].conjugate().transpose()))
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, )))
lead[lat(0)] = H0
lead[lat.neighbors()] = V0
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
down, up = kwant.wave_function(fsyst, energy=1.0)(0)
def M_a(site):
i = site.tag[0]
return ft.reduce(np.dot,
(Us[i], sigmaz, Us[i].conjugate().transpose()))
x_hoppings = kwant.builder.HoppingKind((1, ), lat)
spin_current_gauge = ops.Current(fsyst, M_a, where=list(x_hoppings(syst)))
_test(spin_current_gauge, up, per_el_val=1)
_test(spin_current_gauge, down, per_el_val=-1)
# check the reverse is also true
minus_x_hoppings = kwant.builder.HoppingKind((-1, ), lat)
spin_current_gauge = ops.Current(fsyst,
M_a,
where=list(minus_x_hoppings(syst)))
_test(spin_current_gauge, up, per_el_val=-1)
_test(spin_current_gauge, down, per_el_val=1)
def wf_stat(salt):
syst = dnlr.make_system_all(length, width, dis, str(salt), width_left,
width_right)
sys = syst.finalized()
t_s = dnlr.tranmission_DIY(sys, en)
wf = kwant.wave_function(sys, en)(0)
myDict = {'TM': t_s, 'wf': wf}
completeName = os.path.join('E:/pt/20/', str(salt) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def test_opservables_gauged():
# Test that we get the same answer when we apply a random
# gauge (unitary) transformation to each site. We also
# adjust our definition of the current to match
# this is to get round a bug in test_mask_interpolate (?!) that fails when
# the random number state is altered.
@contextmanager
def save_random_state():
old_state = np.random.get_state()
yield
np.random.set_state(old_state)
L = 20
with save_random_state():
Us = deque([kwant.rmt.circular(2) for i in range(L)])
# need these to get the coupling to the leads right
Us.append(np.eye(2))
Us.appendleft(np.eye(2))
H0 = 2 * np.eye(2) + 0.1 * sigmaz # onsite
V0 = -1 * np.eye(2) # hopping
lat = kwant.lattice.chain(norbs=2)
syst = kwant.Builder()
for i, U in enumerate(Us):
syst[lat(i)] = ft.reduce(np.dot, (U, H0, U.conjugate().transpose()))
for a, b in kwant.builder.HoppingKind((1,), lat)(syst):
i, j = a.tag[0], b.tag[0]
syst[(a, b)] = ft.reduce(np.dot,
(Us[i], V0, Us[j].conjugate().transpose()))
lead = kwant.Builder(kwant.TranslationalSymmetry((-1,)))
lead[lat(0)] = H0
lead[lat.neighbors()] = V0
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
down, up = kwant.wave_function(fsyst, energy=1.0)(0)
def M_a(site):
i = site.tag[0]
return ft.reduce(np.dot,
(Us[i], sigmaz, Us[i].conjugate().transpose()))
x_hoppings = kwant.builder.HoppingKind((1,), lat)
spin_current_gauge = ops.Current(fsyst, M_a, where=x_hoppings(syst))
_test(spin_current_gauge, up, per_el_val=1)
_test(spin_current_gauge, down, per_el_val=-1)
# check the reverse is also true
minus_x_hoppings = kwant.builder.HoppingKind((-1,), lat)
spin_current_gauge = ops.Current(fsyst, M_a, where=minus_x_hoppings(syst))
_test(spin_current_gauge, up, per_el_val=-1)
_test(spin_current_gauge, down, per_el_val=1)
def oscle(ene, lead_nr):
wfs = kwant.wave_function(syst, ene,
check_hermiticity=True)(lead_nr)
spin_current_z = 0
for psi in wfs:
psi_start = psi[0:2]
psi_end = psi[2 * 61:2 * 61 + 2]
#spin_current_z += -2 *imag(psi_end.conjugate().dot(sigma_z).dot(psi_start))
spin_current_z += abs(
imag(psi_end.conjugate().dot(sigma_z).dot(psi_start)))
return spin_current_z
def stat_wf(salt):
wf_spec=np.zeros((f_num,length),dtype=complex)
t_spec=[]
sys=od.make_system(length,dis,str(salt))
sys=sys.finalized()
for i in range(f_num):
wf_spec[i,]=kwant.wave_function(sys,ens[i])(0)
t_spec.append(kwant.smatrix(sys,ens[i]).transmission(1,0))
myDict = {'wf':wf_spec,'t':t_spec}
completeName = os.path.join('E:/pt/5/',str(salt)+'.mat')
sio.savemat(completeName,myDict,oned_as='row')
def dwell(cishu):
salt = cishu #+random.random()*100
# width=49.6
syst = make_system(width, length, str(salt))
attach_lead(syst)
# kwant.plot(syst,fig_size=(25, 30))
sys = syst.finalized()
tt = t_gf(sys)
wf = kwant.wave_function(sys, e1)(0)
t_wf = sum(abs(wf[0])**2) / 2 / np.pi
return [tt, t_wf]
def test_current():
syst = syst_2d().finalized()
J = kwant.operator.Current(syst)
current = J(kwant.wave_function(syst, energy=1)(1)[0])
# Test good codepath
with tempfile.NamedTemporaryFile('w+b') as out:
plotter.current(syst, current, file=out)
fig = pyplot.Figure()
ax = fig.add_subplot(1, 1, 1)
plotter.current(syst, current, ax=ax, file=out)
def lni(cishu):
en = 0.5
salt = cishu + random.random() * 100
sys = make_system(width, length, str(salt))
wff = kwant.wave_function(sys, en)(0)
w = np.abs(wff.T)
coord = np.array([sys.pos(i) for i in range(w.shape[0] // 2)])
up = np.concatenate((coord, w[0::2, ]), axis=1)
down = np.concatenate((coord, w[1::2, ]), axis=1)
myDict = {'u': up, 'd': down}
completeName = os.path.join('E:/dwell2/5/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def current_spin(syst,
parameters,
eF_value=0,
energy=428,
lead_index=0,
spin="up",
colormap="Reds",
axis=None):
"""
Gera mapa da densidade de corrente para elétrons incidentes
da lead esquerda. Se o axis é dado a função gera uma figura
caso contrário somente a array resultante é retornada. Para
se gerar uma figura posterioriormente, o systema deve ser
construído de modo identico àquele usado para calcular a
corrente (syst).
"syst": Note que o sistema é TOTAL com a matriz Hamiltoniana 6x6;
"parameters": dicionario -> define const. para a Hamiltoniana;
"eF_value" : valor da magnitude do campo elétrico em meV;
"energy": potencial eletroquímico dos eletrons incidentes;
"lead_index": "0" para elétrons incidentes da esquerda e "1" para elétrons da direita;
"spin": projeção do pseudo spin
"colormap" = mapa de cores usado para 'plotting'
"axis" = eixo usado para plot, caso seja 'None' a função retorna a array com os valores de corrente mas não gera figura
"""
parameters["eF"] = eF_value
if spin.lower() == "total": up, down = 1, 1
elif spin.lower() == "up": up, down = 1, 0
elif spin.lower() == "down": up, down = 0, 1
sz_sub_matrix = np.array([[up, 0], [0, down]])
Sz_total_matrix = np.kron(sz_sub_matrix, np.eye(3))
wf = kwant.wave_function(syst, energy=energy, params=parameters)
J_spin = kwant.operator.Current(syst, Sz_total_matrix)
current_spin = sum(
J_spin(psi, params=parameters) for psi in wf(lead_index))
# kwant.plotter.current(syst, current_spin, cmap = colormap, colorbar = False, show = False, ax=axis, density=1/9)
if axis != None:
kwant.plotter.current(syst,
current_spin,
cmap=colormap,
colorbar=False,
show=False,
ax=axis)
edit_axis(axis, spin) # change units to nm
return current_spin
def lnt_x1(cishu):
salt = cishu + random()
sys = make_system(length, width, str(salt))
# gf_mode=kwant.smatrix(sys,en).submatrix(1,0)
# t=kwant.smatrix(sys,en).transmission(1,0)
wff = kwant.wave_function(sys, en)(0)
w = np.abs(wff.T)
coord = np.array([sys.pos(i) for i in range(w.shape[0])])
u = np.concatenate((coord, w), axis=1)
myDict = {'u': u}
completeName = os.path.join('E:/dwell2/14/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def lnt_x1(cishu):
en = 0.4
salt = cishu + random()
sys = make_system(length, width, lead_width, str(salt))
sm = kwant.smatrix(sys, en)
gf_mode = sm.submatrix(1, 0)
t = sm.transmission(1, 0)
wff = kwant.wave_function(sys, en)(0)
w = np.abs(wff.T)
coord = np.array([sys.pos(i) for i in range(w.shape[0])])
u = np.concatenate((coord, w), axis=1)
myDict = {'u': u, 't': t, 'g': gf_mode}
completeName = os.path.join('E:/narrowlead/11/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def tau_n(cishu):
en = 0.4
salt = cishu + random.random() * 1000
sys = make_system(length, width, str(salt))
gf_mode = kwant.smatrix(sys, en).submatrix(1, 0)
# s=np.linalg.svd(gf_mode, full_matrices=False, compute_uv=False) #u, s, vh
wf = kwant.wave_function(sys, en)(0)
# kwant.plotter.map(sys, (abs(wf[14])**2),num_lead_cells=5,fig_size=(15, 10),colorbar=False)
ldos = kwant.ldos(sys, en)
if cishu == 0:
coord = np.array([sys.pos(i) for i in range(ldos.shape[0])])
sio.savemat('E:/dwell3/167/coord.mat', {'coord': coord}, oned_as='row')
myDict = {'gf_mode': gf_mode, 'wf': wf, 'ld': ldos}
completeName = os.path.join('E:/dwell3/167/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def TM(cishu):
en = 0.4
salt = cishu + random.random() * 100
syst = make_system(width, length, str(salt))
attach_lead(syst)
sys = syst.finalized()
wf = kwant.wave_function(sys, en)(0)
gf_mode = kwant.smatrix(sys, en).submatrix(1, 0)
# s=np.linalg.svd(gf_mode, full_matrices=False, compute_uv=False) #u, s, vh
ldos = kwant.ldos(sys, en)
if cishu == 0:
coord = np.array([sys.pos(i) for i in range(ldos.shape[0])])
sio.savemat('E:/dwell3/703/coord.mat', {'coord': coord}, oned_as='row')
myDict = {'gf_mode': gf_mode, 'wf': wf, 'ld': ldos} #'s':s,
completeName = os.path.join('E:/dwell3/703/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def analyze_bhz(pot=0, L_barrier=100, shift=0, lead_index=0):
def potential_barrier(x, y):
if abs(x) < L_barrier / 2:
return -(pot - shift)
else:
return 0
params = dict(A=364.5,
B=-686.0,
D=-512.0,
M=-10.0,
C=potential_barrier,
C_const=-shift)
syst = qsh_system()
# get scattering wave functions at E=0
wf = kwant.wave_function(syst, energy=-10, params=params)
# prepare density operators
# sigma_z = np.array([[1, 0], [0, -1]])
prob_density = kwant.operator.Density(syst, np.kron(sigma_z, np.eye(2)))
# J_0 = kwant.operator.Current(syst)
# calculate expectation values and plot them
wf_sqr = sum(prob_density(psi) for psi in wf(lead_index))
print(max(wf_sqr))
# current = sum(J_0(psi,params=params) for psi in wf(lead_index))
fig, (ax1) = plt.subplots(1, 1, figsize=(16, 4))
ax1 = plt.gca()
ax1.set_title(r'$\Psi_{\uparrow}$')
ax1.set_xlabel(r'$x$ [nm]')
ax1.set_ylabel(r'$y$ [nm]')
kwant.plotter.map(syst, (1 / max(wf_sqr)) * wf_sqr,
fig_size=(9, 2),
ax=ax1,
cmap='seismic')
ax = ax1
im = [
obj for obj in ax.get_children()
if isinstance(obj, mpl.image.AxesImage)
][0]
fig.colorbar(im, ax=ax)
plt.tight_layout()
plt.show()
def lnt_x(cishu):
salt = cishu + random()
sys = make_system(width, length, str(salt))
# gf_mode=kwant.smatrix(sys,en).submatrix(1,0)
# t=kwant.smatrix(sys,en).transmission(1,0)
wff = kwant.wave_function(sys, en)
wf = wff(0)
for num_channel in range(wf.shape[0]):
wf1 = wf[num_channel, ]
ans = []
for k in range(len(wf1)):
ans.append(np.append(sys.pos(k), wf1[k]))
myDict = {'ans': ans}
completeName = os.path.join(
'E:/yuhao/65/',
str(cishu * wf.shape[0] + num_channel) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def get_current_with_lead(sys,sysvx,sysvy,hop_sites,pars):
wf = kwant.wave_function(sys, pars.EF, args=[pars])
eva = wf(0)
T = calculate.calculate_conductance(sys, pars.EF, 1, 0, pars)
print T, eva.shape[0]
xs, ys, sites_index, vx_coomatrix, vy_coomatrix = get_core_matrix(sysvx, sysvy, hop_sites, pars)
vx0 = 0;
ev0 = 0;
vy0 = 0;
for i in range(eva.shape[0]):
ev = eva[i, :]
vx, vy = get_current(ev, sites_index, vx_coomatrix, vy_coomatrix)
vx0 = vx + vx0
vy0 = vy + vy0
ev0 = ev0 + np.abs(ev) ** 2
return xs, ys, ev0, vx0, vy0
def TM(cishu):
salt = cishu + random.random() * 100
syst = make_system(width, length, str(salt))
attach_lead(syst)
sys = syst.finalized()
#kwant.plot(sys, fig_size=(10, 3))
wf = kwant.wave_function(sys, 0.4)(0)
# kwant.plotter.map(sys, (abs(wf[14])**2),num_lead_cells=5,fig_size=(15, 10),colorbar=False)
#
# t=kwant.smatrix(sys,.35).transmission(1,0)
gf_mode = kwant.smatrix(sys, 0.4).submatrix(1, 0)
# s=np.linalg.svd(gf_mode, full_matrices=False, compute_uv=False) #u, s, vh
ldos = kwant.ldos(sys, 0.4)
if cishu == 0:
coord = np.array([sys.pos(i) for i in range(ldos.shape[0])])
sio.savemat('E:/dwell3/327/coord.mat', {'coord': coord}, oned_as='row')
myDict = {'gf_mode': gf_mode, 'wf': wf, 'ld': ldos} #'s':s,
completeName = os.path.join('E:/dwell3/327/', str(cishu) + ".mat")
sio.savemat(completeName, myDict, oned_as='row')
def get_current_with_lead(sys, sysvx, sysvy, hop_sites, pars):
wf = kwant.wave_function(sys, pars.EF, args=[pars])
eva = wf(0)
T = calculate.calculate_conductance(sys, pars.EF, 1, 0, pars)
print T, eva.shape[0]
xs, ys, sites_index, vx_coomatrix, vy_coomatrix = get_core_matrix(
sysvx, sysvy, hop_sites, pars)
vx0 = 0
ev0 = 0
vy0 = 0
for i in range(eva.shape[0]):
ev = eva[i, :]
vx, vy = get_current(ev, sites_index, vx_coomatrix, vy_coomatrix)
vx0 = vx + vx0
vy0 = vy + vy0
ev0 = ev0 + np.abs(ev)**2
return xs, ys, ev0, vx0, vy0
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 plot_psi(sys, energy, dx, W, L, args):
wave_f=kwant.wave_function(sys,energy,args)
density_lead_up=(abs(wave_f(0))**2).sum(axis=0)
density_lead_down=(abs(wave_f(1))**2).sum(axis=0)
sites= sys.sites
psi_lead_up= dict(zip(sites, density_lead_up))
psi_lead_down= dict(zip(sites, density_lead_down))
lat_u = kwant.lattice.square(dx, name='up')
lat_d = kwant.lattice.square(dx, name='down')
f=open('psi'+str(energy/f_eV2au)+'.dat','w')
for i in range(0,L):
for j in range(-W+1,W):
f_up=psi_lead_up[lat_u(i,j)]+psi_lead_down[lat_u(i,j)]
f_down=psi_lead_up[lat_d(i,j)]+psi_lead_down[lat_d(i,j)]
f_updown=f_up+f_down
f.write("%e %e %e %e %e\n"%(i*dx/f_nm2au,j*dx/f_nm2au,f_up,f_down,f_updown))
f.write("\n")
f.close()
def test_opservables_scattering():
# Disordered system with two ordered strips on the left/right. We check
# that the current on the right of the disorder due to incoming mode `m` is
# equal to Σ_n |t_nm|^2. Similarly the current on the left of the disorder
# is checked against 1 - Σ_n |r_nm|^2
N = 10
lat, syst = _random_square_system(N)
# add extra sites so we can calculate the current in a region
# where there is no backscattering
syst[(lat(i, j) for i in [-1, N] for j in range(N))] = 2
syst[((lat(-1, j), lat(0, j)) for j in range(N))] = -1
syst[((lat(N - 1, j), lat(N, j)) for j in range(N))] = -1
lat, lead = _perfect_lead(3)
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
fsyst = syst.finalized()
# currents on the left and right of the disordered region
right_interface = [(lat(N, j), lat(N - 1, j)) for j in range(3)]
left_interface = [(lat(0, j), lat(-1, j)) for j in range(3)]
J_right = ops.Current(fsyst, where=right_interface)
J_right_tot = ops.Current(fsyst, where=right_interface, sum=True)
J_left = ops.Current(fsyst, where=left_interface)
J_left_tot = ops.Current(fsyst, where=left_interface, sum=True)
smatrix = kwant.smatrix(fsyst, energy=1.0)
t = smatrix.submatrix(1, 0).T # want to iterate over the columns
r = smatrix.submatrix(0, 0).T # want to iterate over the columns
wfs = kwant.wave_function(fsyst, energy=1.0)(0)
for rv, tv, wf in zip(r, t, wfs):
_test(J_right, wf, reduced_val=np.sum(np.abs(tv)**2))
_test(J_right_tot, wf, per_el_val=np.sum(np.abs(tv)**2))
_test(J_left, wf, reduced_val=(1 - np.sum(np.abs(rv)**2)))
_test(J_left_tot, wf, per_el_val=(1 - np.sum(np.abs(rv)**2)))
def test_phase_sign(system_and_gauge):
syst, gauge = system_and_gauge
peierls, peierls_left, peierls_right = gauge(0.1, 0.1, 0.1)
params = dict(peierls=peierls, peierls_left=peierls_left,
peierls_right=peierls_right)
cut = [(square_lattice(1, j), square_lattice(0, j))
for j in range(10)]
J = kwant.operator.Current(syst, where=cut)
J = J.bind(params=params)
psi = kwant.wave_function(syst, energy=0.6, params=params)(0)[0]
# Electrons incident from the left travel along the *top*
# edge of the Hall bar in the presence of a magnetic field
# out of the plane
j = J(psi)
j_bottom = sum(j[0:5])
j_top = sum(j[5:10])
assert np.isclose(j_top + j_bottom, 1) # sanity check
assert j_top > 0.9
def wave_density(sys, pars, lead_nr=0):
wf = kwant.wave_function(sys, pars.EF, args=[pars])
return (abs(wf(lead_nr))**2).sum(axis=0)
def wave_density(sys, pars, lead_nr=0):
wf = kwant.wave_function(sys, pars.EF, args=[pars])
return (abs(wf(lead_nr))**2).sum(axis=0)
x, y = pos
return abs(y) < width
sym = kwant.TranslationalSymmetry((-1, 0))
sym.add_site_family(graphene.sublattices[0], other_vectors=[(-1, 2)])
sym.add_site_family(graphene.sublattices[1], other_vectors=[(-1, 2)])
lead = kwant.Builder(sym) #,conservation_law=-sz
lead[graphene.shape(lead_shape, (0, width - 1))] = 0
lead[graphene.neighbors()] = 1
# lead[[kwant.builder.HoppingKind(*hopping) for hopping in nnn_hoppings]]=1j *m2
sys.attach_lead(lead)
sys.attach_lead(lead.reversed())
#def gf_virtual(cishu):
syst = make_system(width, length, str(8900))
attach_lead(syst)
sys = syst.finalized()
#kwant.plot(sys, fig_size=(10, 3))
wff = kwant.wave_function(sys, .4)
wf = wff(0)
kwant.plotter.map(sys, (abs(wf[16])),
num_lead_cells=5,
fig_size=(15, 10),
colorbar=False) #
elapsed = time() - t_ini
sys = kwant.Builder()
sys[graphene.shape(disk, (0, 0))] = onsite
sys[graphene.neighbors()] = -1
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
lead[graphene.shape(edge, (0, 0))] = onsite_lead
lead[graphene.neighbors()] = -1
sys.attach_lead(lead)
sys.attach_lead(lead.reversed())
return sys.finalized()
#pyplot.rcParams["figure.figsize"] = [20,10]
#kwant.plot(sys)
sys = make_system()
wf = kwant.wave_function(sys, en)(0)
#wavef1=[]
#for i in range(wf.shape[1]):
# wavef1.append(wf[0,i])
#kwant.plotter.map(sys,(abs(np.array(wavef1))**2), fig_size=(20, 12))
tpp = (abs(wf)**2)[0, ]
kwant.plotter.map(sys, tpp, fig_size=(20, 12))
gf = kwant.greens_function(sys, en).submatrix(1, 0)
t1 = kwant.greens_function(sys, en).transmission(1, 0)
sg = np.linalg.svd(gf, compute_uv=False)
taug1 = sg**2
#gf_measure=np.zeros([14,14],dtype=complex)
#for j in range(14):
def plot_spin(sys, energy, dx, W, L, args):
wave_f=kwant.wave_function(sys, energy, args)
Sxup=[[0 for i in range(-W+1,W)] for j in range(L)]
Syup=[[0 for i in range(-W+1,W)] for j in range(L)]
Szup=[[0 for i in range(-W+1,W)] for j in range(L)]
sites=sys.sites
lat_u = kwant.lattice.square(dx, name='up')
lat_d = kwant.lattice.square(dx, name='down')
#####wpuszczamy spin up
for k in range(len(wave_f(0))):
wf=dict(zip(sites,wave_f(0)[k]))
for i in range(0,L):
for j in range(-W+1,W):
Sxup[i][j]+=wf[lat_u(i,j)].conjugate()*wf[lat_d(i,j)]+wf[lat_d(i,j)].conjugate()*wf[lat_u(i,j)]
Syup[i][j]+=-1j*wf[lat_u(i,j)].conjugate()*wf[lat_d(i,j)]+1j*wf[lat_d(i,j)].conjugate()*wf[lat_u(i,j)]
Szup[i][j]+=wf[lat_u(i,j)].conjugate()*wf[lat_u(i,j)]-wf[lat_d(i,j)].conjugate()*wf[lat_d(i,j)]
del wf
f1=open('spin_up'+str(energy/f_eV2au)+'.dat',"w")
for i in range(0,L):
for j in range(-W+1,W):
f1.write("%e %e %e %e %e %e %e %e\n" % (i*dx/f_nm2au,j*dx/f_nm2au, Sxup[i][j].real, Syup[i][j].real, Szup[i][j].real, Sxup[i][j].imag, Syup[i][j].imag, Szup[i][j].imag))
f1.write("\n")
f1.close()
Sxdn=[[0 for i in range(-W+1,W)] for j in range(L)]
Sydn=[[0 for i in range(-W+1,W)] for j in range(L)]
Szdn=[[0 for i in range(-W+1,W)] for j in range(L)]
#####wpuszczamy spin down
for k in range(len(wave_f(1))):
wf=dict(zip(sites,wave_f(1)[k]))
for i in range(0,L):
for j in range(-W+1,W):
Sxdn[i][j]+=wf[lat_u(i,j)].conjugate()*wf[lat_d(i,j)]+wf[lat_d(i,j)].conjugate()*wf[lat_u(i,j)]
Sydn[i][j]+=-1j*wf[lat_u(i,j)].conjugate()*wf[lat_d(i,j)]+1j*wf[lat_d(i,j)].conjugate()*wf[lat_u(i,j)]
Szdn[i][j]+=wf[lat_u(i,j)].conjugate()*wf[lat_u(i,j)]-wf[lat_d(i,j)].conjugate()*wf[lat_d(i,j)]
del wf
f1=open('spin_down'+str(energy/f_eV2au)+'.dat',"w")
for i in range(0,L):
for j in range(-W+1,W):
f1.write("%e %e %e %e %e %e %e %e\n" % (i*dx/f_nm2au,j*dx/f_nm2au, Sxdn[i][j].real, Sydn[i][j].real, Szdn[i][j].real, Sxdn[i][j].imag, Sydn[i][j].imag, Szdn[i][j].imag))
f1.write("\n")
f1.close()
Sx=[[0 for i in range(-W+1,W)] for j in range(L)]
Sy=[[0 for i in range(-W+1,W)] for j in range(L)]
Sz=[[0 for i in range(-W+1,W)] for j in range(L)]
for i in range(0,L):
for j in range(-W+1,W):
Sx[i][j]=Sxup[i][j]+Sxdn[i][j]
Sy[i][j]=Syup[i][j]+Sydn[i][j]
Sz[i][j]=Szup[i][j]+Szdn[i][j]
f1=open('spin'+str(energy/f_eV2au)+'.dat',"w")
for i in range(0,L):
for j in range(-W+1,W):
f1.write("%e %e %e %e %e %e %e %e\n" % (i*dx/f_nm2au,j*dx/f_nm2au, Sx[i][j].real, Sy[i][j].real, Sz[i][j].real, Sx[i][j].imag, Sy[i][j].imag, Sz[i][j].imag))
f1.write("\n")
f1.close()
