def get_left_channels(self, energy, nchan=1):
self.initialize()
g_s_ii = self.greenfunction.retarded(energy)
lambda_l_ii = self.selfenergies[0].get_lambda(energy)
lambda_r_ii = self.selfenergies[1].get_lambda(energy)
if self.greenfunction.S is not None:
s_mm = self.greenfunction.S
s_s_i, s_s_ii = linalg.eig(s_mm)
s_s_i = np.abs(s_s_i)
s_s_sqrt_i = np.sqrt(s_s_i) # sqrt of eigenvalues
s_s_sqrt_ii = np.dot(s_s_ii * s_s_sqrt_i, dagger(s_s_ii))
s_s_isqrt_ii = np.dot(s_s_ii / s_s_sqrt_i, dagger(s_s_ii))
lambdab_r_ii = np.dot(np.dot(s_s_isqrt_ii, lambda_r_ii), s_s_isqrt_ii)
a_l_ii = np.dot(np.dot(g_s_ii, lambda_l_ii), dagger(g_s_ii))
ab_l_ii = np.dot(np.dot(s_s_sqrt_ii, a_l_ii), s_s_sqrt_ii)
lambda_i, u_ii = linalg.eig(ab_l_ii)
ut_ii = np.sqrt(lambda_i / (2.0 * np.pi)) * u_ii
m_ii = 2 * np.pi * np.dot(np.dot(dagger(ut_ii), lambdab_r_ii), ut_ii)
T_i, c_in = linalg.eig(m_ii)
T_i = np.abs(T_i)
channels = np.argsort(-T_i)[:nchan]
c_in = np.take(c_in, channels, axis=1)
T_n = np.take(T_i, channels)
v_in = np.dot(np.dot(s_s_isqrt_ii, ut_ii), c_in)
return T_n, v_in
def get_transmission(self, v_12, v_11_2=None, v_22_1=None):
"""XXX
v_12:
coupling between tip and surface
v_11_2:
correction to "on-site" tip elements due to the
surface (eq.16). Is only included to first order.
v_22_1:
corretion to "on-site" surface elements due to he
tip (eq.17). Is only included to first order.
"""
dim0 = v_12.shape[0]
dim1 = v_12.shape[1]
nenergies = len(self.energies)
T_e = np.empty(nenergies, float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
if v_11_2 != None:
gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2))
gf1 += gft1 #eq. 16
else:
gf1 = gft1
gft2 = self.gft2_emm[e]
if v_22_1 != None:
gf2 = np.dot(v_22_1, np.dot(gft2, v_22_1))
gf2 += gft2 #eq. 17
else:
gf2 = gft2
a1 = (gf1 - dagger(gf1))
a2 = (gf2 - dagger(gf2))
self.v_12 = v_12
self.a2 = a2
self.v_21 = v_21
self.a1 = a1
v12_a2 = np.dot(v_12, a2[:dim1])
v21_a1 = np.dot(v_21, a1[-dim0:])
self.v12_a2 = v12_a2
self.v21_a1 = v21_a1
T = -np.trace(np.dot(v12_a2[:, :dim1], v21_a1[:, -dim0:])) #eq. 11
assert abs(T.imag).max() < 1e-14
T_e[e] = T.real
self.T_e = T_e
return T_e
def get_transmission(self, v_12, v_11_2=None, v_22_1=None):
"""XXX
v_12:
coupling between tip and surface
v_11_2:
correction to "on-site" tip elements due to the
surface (eq.16). Is only included to first order.
v_22_1:
corretion to "on-site" surface elements due to he
tip (eq.17). Is only included to first order.
"""
dim0 = v_12.shape[0]
dim1 = v_12.shape[1]
nenergies = len(self.energies)
T_e = np.empty(nenergies,float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
if v_11_2!=None:
gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2))
gf1 += gft1 #eq. 16
else:
gf1 = gft1
gft2 = self.gft2_emm[e]
if v_22_1!=None:
gf2 = np.dot(v_22_1,np.dot(gft2, v_22_1))
gf2 += gft2 #eq. 17
else:
gf2 = gft2
a1 = (gf1 - dagger(gf1))
a2 = (gf2 - dagger(gf2))
self.v_12 = v_12
self.a2 = a2
self.v_21 = v_21
self.a1 = a1
v12_a2 = np.dot(v_12, a2[:dim1])
v21_a1 = np.dot(v_21, a1[-dim0:])
self.v12_a2 = v12_a2
self.v21_a1 = v21_a1
T = -np.trace(np.dot(v12_a2[:,:dim1], v21_a1[:,-dim0:])) #eq. 11
assert abs(T.imag).max() < 1e-14
T_e[e] = T.real
self.T_e = T_e
return T_e
def get_transmission(self, v_12):
nenergies = len(self.energies)
T_e = np.empty(nenergies, float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
gft2 = self.gft2_emm[e]
a1 = gft1 - dagger(gft1)
a2 = gft2 - dagger(gft2)
v12_a2 = np.dot(v_12, a2)
v21_a1 = np.dot(v_21, a1)
T = -np.trace(np.dot(v12_a2, v21_a1))
T_e[e] = T
self.T_e = T_e
return T_e
def get_transmission(self, v_12):
nenergies = len(self.energies)
T_e = np.empty(nenergies,float)
v_21 = dagger(v_12)
for e, energy in enumerate(self.energies):
gft1 = self.gft1_emm[e]
gft2 = self.gft2_emm[e]
a1 = (gft1 - dagger(gft1))
a2 = (gft2 - dagger(gft2))
v12_a2 = np.dot(v_12, a2)
v21_a1 = np.dot(v_21, a1)
T = -np.trace(np.dot(v12_a2, v21_a1))
T_e[e] = T
self.T_e = T_e
return T_e
def test_get_gradients(wan, rng):
wanf = wan(nwannier=4, fixedstates=2, kpts=(1, 1, 1),
initialwannier='bloch', std_calc=False)
# create an anti-hermitian array/matrix
step = rng.rand(wanf.get_gradients().size) + \
1.j * rng.rand(wanf.get_gradients().size)
step *= 1e-8
step -= dagger(step)
f1 = wanf.get_functional_value()
wanf.step(step)
f2 = wanf.get_functional_value()
assert (np.abs((f2 - f1) / step).ravel() -
np.abs(wanf.get_gradients())).max() < 1e-4
def lowdin_rotation(self, apply=False):
p = self.input_parameters
h_mm = p['h']
s_mm = p['s']
eig, rot_mm = linalg.eigh(s_mm)
eig = np.abs(eig)
rot_mm = np.dot(rot_mm / np.sqrt(eig), dagger(rot_mm))
if apply:
self.uptodate = False
h_mm[:] = rotate_matrix(h_mm, rot_mm) # rotate C region
s_mm[:] = rotate_matrix(s_mm, rot_mm)
for alpha, sigma in enumerate(self.selfenergies):
sigma.h_im[:] = np.dot(sigma.h_im, rot_mm) # rotate L-C coupl.
sigma.s_im[:] = np.dot(sigma.s_im, rot_mm)
return rot_mm
def update(self):
if self.uptodate:
return
p = self.input_parameters
self.energies = p['energies']
nepts = len(self.energies)
nchan = p['eigenchannels']
pdos = p['pdos']
self.T_e = np.empty(nepts)
if p['dos']:
self.dos_e = np.empty(nepts)
if pdos != []:
self.pdos_ne = np.empty((len(pdos), nepts))
if nchan > 0:
self.eigenchannels_ne = np.empty((nchan, nepts))
for e, energy in enumerate(self.energies):
Ginv_mm = self.greenfunction.retarded(energy, inverse=True)
lambda1_mm = self.selfenergies[0].get_lambda(energy)
lambda2_mm = self.selfenergies[1].get_lambda(energy)
a_mm = linalg.solve(Ginv_mm, lambda1_mm)
b_mm = linalg.solve(dagger(Ginv_mm), lambda2_mm)
T_mm = np.dot(a_mm, b_mm)
if nchan > 0:
t_n = linalg.eigvals(T_mm).real
self.eigenchannels_ne[:, e] = np.sort(t_n)[-nchan:]
self.T_e[e] = np.sum(t_n)
else:
self.T_e[e] = np.trace(T_mm).real
print(energy, self.T_e[e], file=self.log)
self.log.flush()
if p['dos']:
self.dos_e[e] = self.greenfunction.dos(energy)
if pdos != []:
self.pdos_ne[:, e] = np.take(self.greenfunction.pdos(energy),
pdos)
self.uptodate = True
def orthonormality_error(matrix):
return np.abs(dagger(matrix) @ matrix - np.eye(len(matrix))).max()