def __call__(self, energy, flag=None):
if self.data_path is not None and flag is not None:
nid = int(flag[2:])
nid += self.nid_plus
flag = str(flag[:2]) + str(nid)
fd = file(self.data_path[self.direction] + '/' +
self.direction + '/' + flag, 'r')
data = cPickle.load(fd)
return data
else:
if self.energy is None or abs(energy - self.energy) > self.tol:
self.energy = energy
z = energy - self.bias
tau_ij = z * self.hsd_ij.S[self.pk].recover() - \
self.hsd_ij.H[self.s][self.pk].recover()
tau_ji = z * dagger(self.hsd_ij.S[self.pk].recover()) - \
dagger(self.hsd_ij.H[self.s][self.pk].recover())
ginv = self.get_sgfinv(energy)
a_ij = dot(ginv, tau_ij)
mat = dot(tau_ji, a_ij)
#if self.rotation_mat is not None:
# mat = np.dot(self.rotation_mat, mat)
# mat = np.dot(mat, self.rotation_mat.T)
self.sigma = Banded_Sparse_Matrix(complex, mat,
self.hsd_ii.S[self.pk].band_index)
return self.sigma
def get_sgfinv(self, energy):
"""The inverse of the retarded surface Green function"""
z = energy - self.bias
v_00 = Banded_Sparse_Matrix(complex,
None,
self.hsd_ii.S[self.pk].band_index)
v_00.reset_from_others(self.hsd_ii.S[self.pk],
self.hsd_ii.H[self.s][self.pk],
z, -1.0)
v_11 = copy.deepcopy(v_00)
v_10 = z * self.hsd_ij.S[self.pk].recover()- \
self.hsd_ij.H[self.s][self.pk].recover()
v_01 = z * dagger(self.hsd_ij.S[self.pk].recover()) - \
dagger(self.hsd_ij.H[self.s][self.pk].recover())
delta = self.conv + 1
while delta > self.conv:
inv_v_11 = v_11.inv()
a = dot(inv_v_11, v_01)
b = dot(inv_v_11, v_10)
v_01_dot_b = dot(v_01, b)
v_00.reset_minus(v_01_dot_b, full=True)
v_11.reset_minus(dot(v_10, a), full=True)
v_11.reset_minus(v_01_dot_b, full=True)
v_01 = -dot(v_01, a)
v_10 = -dot(v_10, b)
delta = np.abs(v_01).max()
return v_00.inv()
def get_left_channels(self, tp, energy, s, k):
# to get the left scattering channel from lead to scattering region
sigma = self.calculate_sigma(tp, s, k, energy)
g_s_ii = self.calculate_green_function_of_k_point(tp, s, k, energy,
sigma, full=True)
nb = g_s_ii.shape[-1]
dtype = g_s_ii.dtype
lambda_l_ii = np.zeros([nb, nb], dtype)
lambda_r_ii = np.zeros([nb, nb], dtype)
ind = get_matrix_index(tp.hsd.S[0].ll_index[0][-1])
lambda_l_ii[ind.T, ind] = 1.j * (sigma[0].recover() -
sigma[0].recover().T.conj())
ind = get_matrix_index(tp.hsd.S[0].ll_index[1][-1])
lambda_r_ii[ind.T, ind] = 1.j * (sigma[1].recover() -
sigma[1].recover().T.conj())
s_mm = tp.hsd.S[k].recover()
s_s_i, s_s_ii = np.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 = np.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 = np.linalg.eig(m_ii)
T_i = np.abs(T_i)
channels = np.argsort(-T_i)
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_sgfinv(self, energy):
"""The inverse of the retarded surface Green function"""
z = energy - self.bias
v_00 = Banded_Sparse_Matrix(complex, None,
self.hsd_ii.S[self.pk].band_index)
v_00.reset_from_others(self.hsd_ii.S[self.pk],
self.hsd_ii.H[self.s][self.pk], z, -1.0)
v_11 = copy.deepcopy(v_00)
v_10 = z * self.hsd_ij.S[self.pk].recover()- \
self.hsd_ij.H[self.s][self.pk].recover()
v_01 = z * dagger(self.hsd_ij.S[self.pk].recover()) - \
dagger(self.hsd_ij.H[self.s][self.pk].recover())
delta = self.conv + 1
while delta > self.conv:
inv_v_11 = v_11.inv()
a = dot(inv_v_11, v_01)
b = dot(inv_v_11, v_10)
v_01_dot_b = dot(v_01, b)
v_00.reset_minus(v_01_dot_b, full=True)
v_11.reset_minus(dot(v_10, a), full=True)
v_11.reset_minus(v_01_dot_b, full=True)
v_01 = -dot(v_01, a)
v_10 = -dot(v_10, b)
delta = np.abs(v_01).max()
return v_00.inv()
def __call__(self, energy, flag=None):
if self.data_path is not None and flag is not None:
nid = int(flag[2:])
nid += self.nid_plus
flag = str(flag[:2]) + str(nid)
fd = file(
self.data_path[self.direction] + '/' + self.direction + '/' +
flag, 'r')
data = cPickle.load(fd)
return data
else:
if self.energy is None or abs(energy - self.energy) > self.tol:
self.energy = energy
z = energy - self.bias
tau_ij = z * self.hsd_ij.S[self.pk].recover() - \
self.hsd_ij.H[self.s][self.pk].recover()
tau_ji = z * dagger(self.hsd_ij.S[self.pk].recover()) - \
dagger(self.hsd_ij.H[self.s][self.pk].recover())
ginv = self.get_sgfinv(energy)
a_ij = dot(ginv, tau_ij)
mat = dot(tau_ji, a_ij)
#if self.rotation_mat is not None:
# mat = np.dot(self.rotation_mat, mat)
# mat = np.dot(mat, self.rotation_mat.T)
self.sigma = Banded_Sparse_Matrix(
complex, mat, self.hsd_ii.S[self.pk].band_index)
return self.sigma
def get_left_channels(self, tp, energy, s, k):
# to get the left scattering channel from lead to scattering region
sigma = self.calculate_sigma(tp, s, k, energy)
g_s_ii = self.calculate_green_function_of_k_point(tp,
s,
k,
energy,
sigma,
full=True)
nb = g_s_ii.shape[-1]
dtype = g_s_ii.dtype
lambda_l_ii = np.zeros([nb, nb], dtype)
lambda_r_ii = np.zeros([nb, nb], dtype)
ind = get_matrix_index(tp.hsd.S[0].ll_index[0][-1])
lambda_l_ii[ind.T, ind] = 1.j * (sigma[0].recover() -
sigma[0].recover().T.conj())
ind = get_matrix_index(tp.hsd.S[0].ll_index[1][-1])
lambda_r_ii[ind.T, ind] = 1.j * (sigma[1].recover() -
sigma[1].recover().T.conj())
s_mm = tp.hsd.S[k].recover()
s_s_i, s_s_ii = np.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 = np.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 = np.linalg.eig(m_ii)
T_i = np.abs(T_i)
channels = np.argsort(-T_i)
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_lambda(self, energy):
sigma = self(energy)
sigma_mm = sigma.recover()
return 1.j * (sigma_mm - dagger(sigma_mm))
def get_lambda(self, energy):
sigma = self(energy)
sigma_mm = sigma.recover()
return 1.j * (sigma_mm - dagger(sigma_mm))