def _refl_LR(self, d, E, params, complete=True):
'''
create a reflection matrix by rotating scattering matrices into a consistent basis. Note that while the kwant basis is arbitrary, kwant perserves independent modes for conservation laws.
- kwant_smat: kwant.SMatrix object
- d: either -1 or 1 for left/right scattering interface
'''
if self.interpolated(d):
if len(params) > 0:
print(
'warning: params passed to an interpolated function, values will be ignored'
)
if self._Ebounds[0] <= E <= self._Ebounds[1]:
return self.interpolators[d](E)
else:
raise Exception(
f"Energy {E} is outside bounds ({self._Ebounds})")
if self.systs[d] is None:
raise Exception("Right system is not defined")
try:
ksmat = kwant.smatrix(self.systs[d], E, params=params)
except ValueError:
ksmat = kwant.smatrix(
self.systs[d], E + 1e-4,
params=params) # this is to counter a bug in kwant
lead_num = 1 if d == L else 0
modes = ksmat.lead_info[lead_num].wave_functions
wf_in, wf_out = np.split(modes, 2, axis=1)
krmat = ksmat.submatrix(lead_num, lead_num)
return SystemInfo._rotate_smat(krmat, wf_in, wf_out)
def t_wiger(sys, en, df):
s1 = kwant.smatrix(sys, en).data
s2 = kwant.smatrix(sys, en + df).data
# tw=s2.transpose().conj()@(s2-s1)/df
# return np.trace(tw)
p1 = np.angle(np.linalg.det(s1))
p2 = np.angle(np.linalg.det(s2))
return (p2 - p1) / df
def t_mode(sys,e1,df,o,i): # only one mode case
g=kwant.smatrix(sys,e1)
g1=kwant.smatrix(sys,e1+df)
try:
gf=g.submatrix(o,i)
u0, s0, vh0=np.linalg.svd(gf, full_matrices=True, compute_uv=True)
gf1=g1.submatrix(o,i)
u1, s1, vh1=np.linalg.svd(gf1, full_matrices=True, compute_uv=True)
t=np.diag(eigentime(u0,u1,vh0,vh1,df)) # time ,not dos
except:
t=0
return t
def calc_G_11_12_S_A(sys_,
p,
ppar,
i,
var_name,
elapsed_time,
biasenergies_asymm=False):
""" Computing conductance. Returns G_11.
Parameters
----------
sys_ : finalized system with all parts and leads.
p : same parameters as are given to the functions making up the hamiltonian (which is also the parameters given to the kwant.Hamiltonian method).
energies : computed eigenenergies in main().
biasenergies_symm : is True if an odd number of biasenergies where every negative value has a corresponding positive value at the same number of places from the value zero, and vice versa. E.g. biasenergies = -3,-2,-1,0,1,2,3. Is False by default. User needs to ensure that biasenergies are "symmetric" like this before entering biasenergies_symm=True as input.
Notes
-----
- if ppar.Sclead = True, SC lead is attached to the middle region. The lead index for the SC lead is 2, because it is atted after the normal leads. Thus, use index 2 if wanting to access the SC lead values in e.g. the smatrix.
"""
print("%.0f'th %s-value, Dt=%.1f" % (i, var_name, elapsed_time))
G_11 = []
G_12 = []
if ppar.oneNLead == True: # One lead means no nonlocal conductance is to be calculated
for biasenergy in p.biasenergies:
smatrix = kwant.smatrix(sys_, biasenergy,
args=[p]) #Takes longer for larger system
G_11.append(2 - \
smatrix.transmission((0,0),(0,0)) + \
smatrix.transmission((0,1),(0,0)))
else:
for biasenergy in p.biasenergies:
smatrix = kwant.smatrix(sys_, biasenergy,
args=[p]) #Takes longer for larger system
# New in kwant version 1.4: args=[p]-->params=[p] inside kwant.smatrix
G_11.append(2 - \
smatrix.transmission((0,0),(0,0)) + \
smatrix.transmission((0,1),(0,0)))
G_12.append( - smatrix.transmission((0,0),(1,0)) + \
smatrix.transmission((0,1),(1,0)))
G_11_S = [(G_11[i] + G_11[-1 - i]) / 2. for i in range(0, len(G_11))]
G_11_A = [(G_11[i] - G_11[-1 - i]) / 2. for i in range(0, len(G_11))]
G_12_S = [(G_12[i] + G_12[-1 - i]) / 2. for i in range(0, len(G_12))]
G_12_A = [(G_12[i] - G_12[-1 - i]) / 2. for i in range(0, len(G_12))]
return G_11, G_12, G_11_S, G_11_A, G_12_S, G_12_A
def test_multiterminal_input():
"""Input checks for two_terminal_shotnoise"""
syst = twoterminal_system()
syst.attach_lead(syst.leads[0].builder)
sol = kwant.smatrix(syst.finalized(), out_leads=[0], in_leads=[0])
raises(ValueError, two_terminal_shotnoise, sol)
def ConductanceAndTV(args_dict, junction):
voltage = args_dict['voltage']
S_matrix = kwant.smatrix(junction, voltage, check_hermiticity=False)
R = S_matrix.submatrix(0, 0)
if (args_dict['multiband'] == 0):
G = 2.0
for (i, j) in [(0, 0), (0, 1), (1, 0), (1, 1)]:
G = G - abs(R[i, j])**2 + abs(R[2 + i, j])**2
else:
G = 4.0
for (i, j) in [(0, 0), (0, 1), (1, 0), (1, 1)]:
G = G - abs(R[i, j])**2 - abs(R[2 + i, j])**2 - abs(
R[2 + i, 2 + j])**2 - abs(R[i, 2 + j])**2 + abs(
R[4 + i, j])**2 + abs(R[4 + i + 2, j])**2 + abs(
R[4 + i, j + 2])**2 + abs(R[4 + i + 2, j + 2])**2
tv0 = LA.det(R)
basis_wf = S_matrix.lead_info[0].wave_functions
normalize_dict = {0: 0, 1: 0, 2: 3, 3: 3, 4: 0, 5: 0, 6: 3, 7: 3}
phase_dict = {}
for n in range(8):
m = normalize_dict[n]
phase_dict[n] = (-1)**m * basis_wf[m, n] / abs(basis_wf[m, n])
tv = tv0 * np.conjugate(
phase_dict[0] * phase_dict[1] * phase_dict[2] * phase_dict[3]
) * phase_dict[4] * phase_dict[5] * phase_dict[6] * phase_dict[7]
return G, tv
def plot_conductance_vs_disorder(bar, energy):
probabilities = np.linspace(0, 0.1, 20)
disorder = 500
conductances = []
errors = []
for counter, prob in enumerate(probabilities):
print(counter),
cond = []
n_sim = 100
for i in range(n_sim):
seed = str(np.random.rand())
smatrix = kwant.smatrix(bar, energy, args = [disorder, prob, seed])
cond.append(smatrix.transmission(1, 0))
conductances.append(np.average(cond))
errors.append(np.std(cond))
ax = plt.subplot(111)
# ax.set_xscale('log')
ax.errorbar(probabilities, conductances, yerr=errors)
# ax.set_xlim(xmin=1)
ax.set_ylim(ymin=-0.1, ymax=1.1)
plt.show()
out = open('conductances_plot', 'wb')
np.savez(out, probabilities=probabilities, conductances=conductances, errors=errors)
def con(n):
en=energies[n]
gf=kwant.greens_function(sys,en).submatrix(1,0)
t=kwant.smatrix(sys,en).transmission(1,0)
myDict = {'gf':gf,'t':t}
completeName = os.path.join('E:/fano/15/', str(n)+".mat")
sio.savemat(completeName,myDict,oned_as='row')
def trans_all(sys, e1):
t = kwant.smatrix(sys, e1)
t10 = t.transmission(1, 0)
t01 = t.transmission(0, 1)
t00 = t.transmission(0, 0)
t11 = t.transmission(1, 1)
return np.array([t10, t01, t00, t11])
def getSMatrix(parameters, junction):
vBias = parameters['vBias']
sMatrix = kwant.smatrix(junction,
parameters['vBias'],
check_hermiticity=False)
R = sMatrix.data
basis_wf = sMatrix.lead_info[0].wave_functions
normalize_dict = {0: 0, 1: 0, 2: 3, 3: 3, 4: 0, 5: 0, 6: 3, 7: 3}
phase_dict = {}
for n in range(8):
m = normalize_dict[n]
phase_dict[n] = (-1)**m * basis_wf[m, n] / abs(basis_wf[m, n])
fixphase = np.conjugate(
phase_dict[0] * phase_dict[1] * phase_dict[2] * phase_dict[3]
) * phase_dict[4] * phase_dict[5] * phase_dict[6] * phase_dict[7]
R = R
TVL, TVR = LA.det(R[:4, :4]), LA.det(R[4:, 4:])
assert (np.imag(TVL) < 1e-10 and np.imag(TVR) < 1e-10
), 'TVL and TVR are not real with the imag=({:e},{:e})'.format(
np.imag(TVL), np.imag(TVR))
TVL, TVR = np.real((fixphase * TVL, fixphase * TVR))
return R, TVL, TVR
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 conductances(
self,
bValues=np.linspace(0, 1.0, 201),
energies=[1e-6 * i for i in range(-120, 120)],
):
syst = NISIN(self.parameters)
data = []
critB = 0
for energy in tqdm(
energies,
desc="Cond",
):
cond = []
for b in bValues:
self.parameters["B"] = b
smatrix = kwant.smatrix(syst, energy, params=self.parameters)
conduct = (
smatrix.submatrix((0, 0), (0, 0)).shape[0] # N
- smatrix.transmission((0, 0), (0, 0)) # R_ee
+ smatrix.transmission((0, 1), (0, 0)) # R_he
)
cond.append(conduct)
if (np.isclose(energy, 0, rtol=1e-6) and critB == 0
and np.abs(2 - conduct) < 0.01):
critB = b
data.append(cond)
outcome = dict(B=bValues, BiasV=energies, Cond=data, CritB=critB)
return outcome
def conductance(syst, energies):
# Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(syst, energy)
data.append(smatrix.transmission(1, 0))
return data
def spec(cishu):
# t=dnlr.tranmission_DIY(sys,ens[cishu])
t = kwant.smatrix(sys, ens[cishu]).submatrix(1, 0)
myDict = {'t': t}
completeName = os.path.join('E:/channel time/63/' + str(cishu) +
'.mat') #7_tracet
sio.savemat(completeName, myDict, oned_as='row')
def transmission(a,cishu):
salt=np.random.randint(10000)
# salt=5
sys = make_cuboid(a,str(salt))
gf_mode = kwant.smatrix(sys, en)
T=gf_mode.transmission(1,0)
return T
def test_multiterminal_input():
"""Input checks for two_terminal_shotnoise"""
sys = twoterminal_system()
sys.attach_lead(sys.leads[0].builder)
sol = kwant.smatrix(sys.finalized(), out_leads=[0], in_leads=[0])
assert_raises(ValueError, two_terminal_shotnoise, sol)
def andreev_conductance(syst, params, E):
"""The Andreev conductance is N - R_ee + R_he."""
smatrix = kwant.smatrix(syst, energy=E, params=params)
r_ee = smatrix.transmission((0, 0), (0, 0))
r_he = smatrix.transmission((0, 1), (0, 0))
N_e = smatrix.submatrix((0, 0), (0, 0)).shape[0]
return N_e - r_ee + r_he
def plot_conductance(syst, energies, L_barrier=100, pot=0, shift=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)
# Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(syst, energy, params=params)
data.append(smatrix.transmission(1, 0))
plt.figure()
plt.plot(energies, data, linestyle='', marker='o', color='red')
plt.xlabel(r"E$_F$ [meV]")
plt.ylabel(r"conductance $[e^2/h]$")
plt.show()
def test_ModesLead_and_SelfEnergyLead():
lat = builder.SimpleSiteFamily()
hoppings = [builder.HoppingKind((1, 0), lat),
builder.HoppingKind((0, 1), lat)]
rng = Random(123)
L = 5
t = 1
energies = [0.9, 1.7]
syst = builder.Builder()
for x in range(L):
for y in range(L):
syst[lat(x, y)] = 4 * t + rng.random() - 0.5
syst[hoppings] = -t
# Attach a lead from the left.
lead = builder.Builder(VerySimpleSymmetry(-1))
for y in range(L):
lead[lat(0, y)] = 4 * t
lead[hoppings] = -t
syst.attach_lead(lead)
# Make the right lead and attach it.
lead = builder.Builder(VerySimpleSymmetry(1))
for y in range(L):
lead[lat(0, y)] = 4 * t
lead[hoppings] = -t
syst.attach_lead(lead)
fsyst = syst.finalized()
ts = [kwant.smatrix(fsyst, e).transmission(1, 0) for e in energies]
# Replace lead with it's finalized copy.
lead = fsyst.leads[1]
interface = [lat(L-1, lead.sites[i].tag[1]) for i in range(L)]
# Re-attach right lead as ModesLead.
syst.leads[1] = builder.ModesLead(lead.modes, interface)
fsyst = syst.finalized()
ts2 = [kwant.smatrix(fsyst, e).transmission(1, 0) for e in energies]
assert_almost_equal(ts2, ts)
# Re-attach right lead as SelfEnergyLead.
syst.leads[1] = builder.SelfEnergyLead(lead.selfenergy, interface)
fsyst = syst.finalized()
ts2 = [kwant.greens_function(fsyst, e).transmission(1, 0) for e in energies]
assert_almost_equal(ts2, ts)
def calculate_transmission(W, params, nsamples):
def disorder(x,y):
return np.random.uniform(-W/2, W/2)
params['V'] = disorder
t1 = []
t2 = []
t3 = []
for k in range(nsamples):
print_t("Calculating transmissions for W={0}, sample {1}".format(W, k))
t1.append(kwant.smatrix(syst, energy=e_1, params=params).transmission(1,0))
t2.append(kwant.smatrix(syst, energy=e_2, params=params).transmission(1,0))
t3.append(kwant.smatrix(syst, energy=e_3, params=params).transmission(1,0))
return [[np.mean(t1), np.std(t1)], [np.mean(t2), np.std(t2)], [np.mean(t3), np.std(t3)]]
def spec(cishu):
# t=dn2.tranmission_DIY(sys,ens[cishu])
t = kwant.smatrix(sys, ens[cishu]).submatrix(1,
0) #,check_hermiticity=False
myDict = {'t': t}
completeName = os.path.join('E:/channel time/102/' + str(cishu) +
'.mat') #7_tracet
sio.savemat(completeName, myDict, oned_as='row')
def plot_local_dos(bar, energy, disorder, probability, seed):
smatrix = kwant.smatrix(bar, energy, args = [disorder, probability, seed])
print('seed : {}, transmission: {}'.format(seed, smatrix.transmission(1, 0)))
local_dos = kwant.ldos(bar, energy=energy, args=[disorder, probability, seed])
kwant.plot(bar, #site_color = -local_dos,
site_color=np.minimum(-np.log(local_dos), 10*np.ones_like(local_dos)),
hop_color='white', cmap='afmhot')
def conductance_matrix(sys, energy, args=()):
n = len(sys.leads)
s = kwant.smatrix(sys, energy, args)
cond = np.array([[s.transmission(i, j) for j in range(n)]
for i in range(n)])
# Correct the reflection blocks, so that rows and columns sum to zero.
cond -= np.diag(cond.sum(axis=0))
return cond
def test_pickling():
syst = kwant.Builder()
lead = kwant.Builder(symmetry=kwant.TranslationalSymmetry([1.]))
lat = kwant.lattice.chain()
syst[lat(0)] = syst[lat(1)] = 0
syst[lat(0), lat(1)] = 1
lead[lat(0)] = syst[lat(1)] = 0
lead[lat(0), lat(1)] = 1
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
syst_copy1 = copy.copy(syst).finalized()
syst_copy2 = pickle.loads(pickle.dumps(syst)).finalized()
syst = syst.finalized()
syst_copy3 = copy.copy(syst)
syst_copy4 = pickle.loads(pickle.dumps(syst))
s = kwant.smatrix(syst, 0.1)
for other in (syst_copy1, syst_copy2, syst_copy3, syst_copy4):
assert np.all(kwant.smatrix(other, 0.1).data == s.data)
def test_pickling():
syst = kwant.Builder()
lead = kwant.Builder(symmetry=kwant.TranslationalSymmetry([1.]))
lat = kwant.lattice.chain()
syst[lat(0)] = syst[lat(1)] = 0
syst[lat(0), lat(1)] = 1
lead[lat(0)] = syst[lat(1)] = 0
lead[lat(0), lat(1)] = 1
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
syst_copy1 = copy.copy(syst).finalized()
syst_copy2 = pickle.loads(pickle.dumps(syst)).finalized()
syst = syst.finalized()
syst_copy3 = copy.copy(syst)
syst_copy4 = pickle.loads(pickle.dumps(syst))
s = kwant.smatrix(syst, 0.1)
for other in (syst_copy1, syst_copy2, syst_copy3, syst_copy4):
assert np.all(kwant.smatrix(other, 0.1).data == s.data)
def s_matrix(sys, energies):
"""Compute the S-Matrix as a function of energy.
Return a list of s of type
<class 'kwant.solvers.common.SMatrix'>.
"""
s = []
for energy in energies:
s.append(kwant.smatrix(sys, energy))
return s
def trans_spin_up(cishu):
en = 0.5
salt = cishu + random.random() * 100
sys = make_system2(width, length, str(salt))
tm = kwant.smatrix(sys, en)
t10_uu = tm.transmission((1, 0), (0, 0))
# t10_du=tm.transmission((1, 1), (0, 0))
# t00_uu=tm.transmission((0, 0), (0, 0))
# t00_du=tm.transmission((0, 1), (0, 0))
return np.array([t10_uu, salt]) #t10_du,t00_uu,t00_du,
def plot_conductance(syst, energies): # Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(syst, energy)
data.append(smatrix.transmission(1, 0))
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [$e^2/h$]")
pyplot.show()
def main():
sys = System((10, 5), 1)
energies = [0.04 * i for i in xrange(100)]
data = [kwant.smatrix(sys, energy).transmission(1, 0)
for energy in energies]
pyplot.plot(energies, data)
pyplot.xlabel("energy [in units of t]")
pyplot.ylabel("conductance [in units of e^2/h]")
pyplot.show()
def plot_conductance(sys, energies):
# Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(sys, energy)
# Conductance is N - R_ee + R_he
data.append(
smatrix.submatrix(0, 0).shape[0] - smatrix.transmission(0, 0) +
smatrix.transmission(1, 0))
pyplot.plot(data)
def test_twoterminal():
"""Shot noise in a two-terminal conductor"""
fsys = twoterminal_system().finalized()
sol = kwant.smatrix(fsys)
t = sol.submatrix(1, 0)
Tn = np.linalg.eigvalsh(np.dot(t, t.conj().T))
noise_should_be = np.sum(Tn * (1 - Tn))
assert_almost_equal(noise_should_be, two_terminal_shotnoise(sol))
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 test_twoterminal():
"""Shot noise in a two-terminal conductor"""
fsyst = twoterminal_system().finalized()
sol = kwant.smatrix(fsyst)
t = sol.submatrix(1, 0)
Tn = np.linalg.eigvalsh(np.dot(t, t.conj().T))
noise_should_be = np.sum(Tn * (1 - Tn))
assert_almost_equal(noise_should_be, two_terminal_shotnoise(sol))
def plot_conductance(sys, energies):
# Compute transmission as a function of energy
data = []
for energy in energies:
smatrix = kwant.smatrix(sys, energy)
data.append(smatrix.transmission(0, 1))
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def plot_conductance(sys, energies):
# Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(sys, energy)
data.append(smatrix.transmission(1, 0))
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def plot_conductance(sys, energies):
data = []
for energy in energies:
smatrix = kwant.smatrix(sys, energy)
data.append(smatrix.transmission(2, 0)+smatrix.transmission(3, 0)+smatrix.transmission(2, 1)+smatrix.transmission(3, 1))
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def plot_conductance(i,j):
# Compute conductance
wb=Workbook()
sh=wb.active
sh.title="ads"
syst = make_system(i,j,acos(1/sqrt(3)),40,40)
smatrix = kwant.smatrix(syst, 0, args=["=.="])
sh.cell(row=i+1,column=1).value=i
#sh.cell(row=i+1,column=2).value=smatrix.transmission(3,0)
sh.cell(row=i+1,column=j+2).value=smatrix.transmission(0,3)
wb.save("2_node_Weyl"+str(i)+"_"+str(j)+".xlsx")
def calculate_conductance(sys,Ef, out_leads, in_leads, pars):
"""
:param
sys : 利用kwant产生的体系
EF : 费米能的大小
out_leads : 电子出射的导线 序列或者是一个整数
in_leads : 入射的导线 序列或者是一个整数
:return
T: kwant.solvers.common.SMatrix ，如果只有单个入射出射导线的话就是一个实数
"""
smatrix = kwant.smatrix(sys, Ef, args=[pars] )
T = smatrix.transmission(out_leads, in_leads)
return T
def plot_conductance(sys, energy, welldepths):
#HIDDEN_BEGIN_sqvr
# Compute conductance
data = []
for welldepth in welldepths:
smatrix = kwant.smatrix(sys, energy, args=[-welldepth])
data.append(smatrix.transmission(1, 0))
pyplot.figure()
pyplot.plot(welldepths, data)
pyplot.xlabel("well depth [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def plot_conductance(syst, energy, fluxes):
# compute conductance
normalized_fluxes = [flux / (2 * pi) for flux in fluxes]
data = []
for flux in fluxes:
smatrix = kwant.smatrix(syst, energy, args=[flux])
data.append(smatrix.transmission(1, 0))
pyplot.figure()
pyplot.plot(normalized_fluxes, data)
pyplot.xlabel("flux [flux quantum]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def plot_conductance(syst, energies):
# Compute conductance
data = []
for energy in energies:
smatrix = kwant.smatrix(syst, energy)
# Conductance is N - R_ee + R_he
data.append(smatrix.submatrix(0, 0).shape[0] -
smatrix.transmission(0, 0) +
smatrix.transmission(1, 0))
#HIDDEN_END_jbjt
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
def transport(ht,energy):
"""Define a Kwant heterostructure using an input one"""
# create kwant objects
lat = kwant.lattice.square()
sys = kwant.Builder()
# create the two leads
sym_L = kwant.TranslationalSymmetry((-1, 0))
sym_R = kwant.TranslationalSymmetry((1, 0))
lead_L = kwant.Builder(sym_L) # create the lead
lead_R = kwant.Builder(sym_R) # create the lead
lead_R[lat(0,0)] = ht.right_intra
lead_L[lat(0,0)] = ht.left_intra
lead_R[lat(0,0),lat(1,0)] = ht.right_inter
# lead_R[lat.neighbors()] = ht.right_inter
lead_L[lat(0,0),lat(-1,0)] = ht.left_inter
# lead_L[lat.neighbors()] = ht.left_inter
# The scattering region will be three sites
# add the onsites of the leads
if not ht.block_diagonal: # dense scattering region
# and create the coupling to the central region
# create central and scattering regions
sys[lat(-1,0)] = ht.left_intra
sys[lat(1,0)] = ht.right_intra
sys[lat(0,0)] = ht.central_intra
sys[lat(0,0), lat(-1,0)] = ht.left_coupling
sys[lat(0,0), lat(1,0)] = ht.right_coupling
# now attach the two leads
sys.attach_lead(lead_L, lat(-1, 0))
sys.attach_lead(lead_R, lat(1, 0))
else: # block diagonal form
nb = len(ht.central_intra)
sys[lat(-1,0)] = ht.left_intra
sys[lat(nb,0)] = ht.right_intra
for i in range(nb):
sys[lat(i,0)] = ht.central_intra[i][i]
for i in range(nb-1):
sys[lat(i,0),lat(i+1,0)] = ht.central_intra[i][i+1]
sys[lat(0,0), lat(-1,0)] = ht.left_coupling
sys[lat(nb-1,0), lat(nb,0)] = ht.right_coupling
sys.attach_lead(lead_L, lat(-1, 0))
sys.attach_lead(lead_R, lat(nb, 0))
sys = sys.finalized()
# kwant.plot(sys)
smatrix = kwant.smatrix(sys, energy)
return smatrix.transmission(1, 0)
def test_qhe(W=16, L=8):
def central_region(pos):
x, y = pos
return -L < x < L and abs(y) < W - 5.5 * math.exp(-x**2 / 5**2)
lat = kwant.lattice.square()
syst = kwant.Builder()
syst[lat.shape(central_region, (0, 0))] = onsite
syst[lat.neighbors()] = hopping
lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))
lead[(lat(0, y) for y in range(-W + 1, W))] = 4
lead[lat.neighbors()] = hopping
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
syst = syst.finalized()
#### The following chunk of code can be uncommented to visualize the
#### conductance plateaus.
# from matplotlib import pyplot
# import numpy
# reciprocal_phis = numpy.linspace(0.1, 7, 200)
# conductances = []
# for phi in 1 / reciprocal_phis:
# smatrix = kwant.smatrix(syst, 1.0, [phi, ""])
# conductances.append(smatrix.transmission(1, 0))
# pyplot.plot(reciprocal_phis, conductances)
# pyplot.show()
for r_phis, T_nominal, max_err in [((1.3, 2.1), 1, 1e-7),
((3.2, 3.7), 2, 1e-3),
((5.2, 5.5), 3, 1e-1)]:
for r_phi in r_phis:
args = (1.0 / r_phi, "")
pc = syst.precalculate(1.0, args, what='all')
for result in [kwant.smatrix(pc, 1, args),
kwant.solvers.default.greens_function(pc, 1, args)]:
assert abs(T_nominal - result.transmission(1, 0)) < max_err
def calc_transmission(system, energy, v=None):
args = [v] if v is not None else ()
smatrix = kwant.smatrix(system, energy, args=args)
return smatrix.transmission(1, 0)
def transmission(self, start_energy, end_energy, number_of_points=500,
print_to_commandline=True):
"""Calculate transmission through system.
Calculates the transmission in `number_of_points` equidistant points
on the intervall [`start_energy`, `end_energy`).
Parameters
----------
wire : :class:`~garn.Wire2D` or :class:`~garn.Wire3D`
The wire model for with the transmission is calculated and
energy and transmission attributes are changed.
start_energy : float
end_energy : float, optional
number_of_points : int, optional
print_to_commandline : bool
If true the resulting transmission energy pairs are printed
in the terminal. (Default Ture beacuse good for monitoring progress)
Notes
-----
The energy is given in units of :math:`t`.
.. math::
t = \dfrac{\hbar^2}{2 m_e^* step\_length^2}
:math:`m_e^*` is the effective mass of the semiconduction and step_length
is the discretization step that is set on initialization of
:class:`~garn.Wire2D` and :class:`~garn.Wire3D` instanses.
The transmission is given in units of :math:`\dfrac{e^2}{\hbar}`.
The function changes the attributes energy and transmission of
*wire* and saves to the file "data-" + `wire.identifier`. If the
transmission function have been called before or the wire.energies
attribute is non-empty the
:meth:`~garn.system_wide._energy_exist_dialog` is called asking
what to do.
"""
# handel case when the wire has calculated before
if self.energies != []:
if (not _energy_exist_dialog()):
return
intervall_length = end_energy - start_energy
stepsize = intervall_length / float(number_of_points)
start_step = int(start_energy / float(stepsize))
end_step = int(end_energy / float(stepsize))
self.energies = [stepsize * i for i in range(start_step, end_step)]
self.transmission_data = []
in_leads, out_leads = self._in_out_nums()
if print_to_commandline:
print("Transmission_Data calculated for energies [t]: ")
for en in self.energies:
smatrix = kwant.smatrix(self.sys, en, in_leads=in_leads,
out_leads=out_leads)
con_tot = 0
for i in range(0,len(in_leads)):
for j in range(len(in_leads), len(in_leads) +
len(out_leads)):
con = smatrix.transmission(j, i)
con_tot = con_tot + con
#print(str(i) + "-" + str(j) + "= " + str(con))
self.transmission_data.append(con_tot)
self._save_to_file(en, con_tot)
if print_to_commandline:
print(str(en) + " " + str(con_tot))
def main():
syst = make_system(100)
print(kwant.smatrix(syst, 1.1, [0.1]).transmission(0, 1))
def test_hamiltonian_submatrix():
sys = kwant.Builder()
chain = kwant.lattice.chain()
for i in xrange(3):
sys[chain(i)] = 0.5 * i
for i in xrange(2):
sys[chain(i), chain(i + 1)] = 1j * (i + 1)
sys2 = sys.finalized()
mat = sys2.hamiltonian_submatrix()
assert mat.shape == (3, 3)
# Sorting is required due to unknown compression order of builder.
perm = np.argsort(sys2.onsite_hamiltonians)
mat_should_be = np.array([[0, 1j, 0], [-1j, 0.5, 2j], [0, -2j, 1]])
mat = mat[perm, :]
mat = mat[:, perm]
np.testing.assert_array_equal(mat, mat_should_be)
mat = sys2.hamiltonian_submatrix(sparse=True)
assert sparse.isspmatrix_coo(mat)
mat = mat.todense()
mat = mat[perm, :]
mat = mat[:, perm]
np.testing.assert_array_equal(mat, mat_should_be)
mat = sys2.hamiltonian_submatrix((), perm[[0, 1]], perm[[2]])
np.testing.assert_array_equal(mat, mat_should_be[:2, 2:3])
mat = sys2.hamiltonian_submatrix((), perm[[0, 1]], perm[[2]], sparse=True)
mat = mat.todense()
np.testing.assert_array_equal(mat, mat_should_be[:2, 2:3])
# Test for correct treatment of matrix input.
sys = kwant.Builder()
sys[chain(0)] = np.array([[0, 1j], [-1j, 0]])
sys[chain(1)] = np.array([[1]])
sys[chain(2)] = np.array([[2]])
sys[chain(1), chain(0)] = np.array([[1, 2j]])
sys[chain(2), chain(1)] = np.array([[3j]])
sys2 = sys.finalized()
mat_dense = sys2.hamiltonian_submatrix()
mat_sp = sys2.hamiltonian_submatrix(sparse=True).todense()
np.testing.assert_array_equal(mat_sp, mat_dense)
# Test precalculation of modes.
np.random.seed(5)
lead = kwant.Builder(kwant.TranslationalSymmetry((-1,)))
lead[chain(0)] = np.zeros((2, 2))
lead[chain(0), chain(1)] = np.random.randn(2, 2)
sys.attach_lead(lead)
sys2 = sys.finalized()
smatrix = kwant.smatrix(sys2, .1).data
sys3 = sys2.precalculate(.1, what='modes')
smatrix2 = kwant.smatrix(sys3, .1).data
np.testing.assert_almost_equal(smatrix, smatrix2)
assert_raises(ValueError, kwant.solvers.default.greens_function, sys3, 0.2)
# Test for shape errors.
sys[chain(0), chain(2)] = np.array([[1, 2]])
sys2 = sys.finalized()
assert_raises(ValueError, sys2.hamiltonian_submatrix)
assert_raises(ValueError, sys2.hamiltonian_submatrix, sparse=True)
sys[chain(0), chain(2)] = 1
sys2 = sys.finalized()
assert_raises(ValueError, sys2.hamiltonian_submatrix)
assert_raises(ValueError, sys2.hamiltonian_submatrix, sparse=True)
# Test for passing parameters to hamiltonian matrix elements
def onsite(site, p1, p2=0):
return site.pos + p1 + p2
def hopping(site1, site2, p1, p2=0):
return p1 - p2
sys = kwant.Builder()
sys[(chain(i) for i in xrange(3))] = onsite
sys[((chain(i), chain(i + 1)) for i in xrange(2))] = hopping
sys2 = sys.finalized()
mat = sys2.hamiltonian_submatrix((2, 1))
mat_should_be = [[3, 1, 0], [1, 4, 1], [0, 1, 5]]
# Sorting is required due to unknown compression order of builder.
onsite_hamiltonians = mat.flat[::4]
perm = np.argsort(onsite_hamiltonians)
mat = mat[perm, :]
mat = mat[:, perm]
np.testing.assert_array_equal(mat, mat_should_be)
pasma(W, dx, m, alfa, Fz, Bx, By, Bz, 0.2/f_nm2au, 1000, Vg1, Vg2, 0)
sys=make_system_SOI(W, L, dx, m, alfa, Fz, Bx, By, Bz, Vg1, Vg2)
#kwant.plot(sys)
#Obliczenie ladunku
#energy=1.0e-3*f_eV2au
#plot_psi(sys, energy, dx, W, L, [dx, m, alfa, Fz, Bx, By, Bz, Vg1, Vg2])
#plot_spin(sys, energy, dx, W, L, [dx, m, alfa, Fz, Bx, By, Bz, Vg1, Vg2])
##Obliczenie konduktancji
f1=open("G.dat","w")
f2=open("T.dat","w")
dE=0.01e-3*f_eV2au
ne=500
for ie in range(ne):
print(ie)
energy = dE+ie*dE
smatrix = kwant.smatrix(sys, energy, [dx, m, alfa, Fz, Bx, By, Bz, Vg1, Vg2])
tupup=smatrix.transmission(2, 0)
tupdown=smatrix.transmission(3, 0)
tdownup=smatrix.transmission(2, 1)
tdowndown=smatrix.transmission(3, 1)
j_up=tupup+tdownup
j_down=tdowndown+tupdown
f2.write("%e %e %e %e %e %e\n"%(energy/f_eV2au, tupup, tupdown, tdownup, tdowndown, tupup + tupdown + tdownup + tdowndown))
f1.write("%e %e %e %e\n"%(energy/f_eV2au, j_up, j_down, j_up+j_down))
f1.close()
f2.close()
#HIDDEN_END_wsgh
# Finalize the system
#HIDDEN_BEGIN_dngj
sys = sys.finalized()
#HIDDEN_END_dngj
# Now that we have the system, we can compute conductance
#HIDDEN_BEGIN_buzn
energies = []
data = []
for ie in xrange(100):
energy = ie * 0.01
# compute the scattering matrix at a given energy
smatrix = kwant.smatrix(sys, energy)
# compute the transmission probability from lead 0 to
# lead 1
energies.append(energy)
data.append(smatrix.transmission(1, 0))
#HIDDEN_END_buzn
# Use matplotlib to write output
# We should see conductance steps
#HIDDEN_BEGIN_lliv
pyplot.figure()
pyplot.plot(energies, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()