def test_construction():
"""
Test that we can construct a NEGF instance, without performing
any operation.
"""
foo = pynegf.PyNegf()
assert(foo is not None)
def test_current_conservation_dephasing(coupling=None):
""" Test that we have current conservation at the electrodes """
currents = []
for orthogonal in [True, False]:
for (ni, nf) in [(1, 2), (2, 1)]:
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(nsites=50,
contact_size=10,
coupling=1.0)
if orthogonal:
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(50)
else:
negf.set_hamiltonian(mat_csr)
mat_csr = utils.orthogonal_linear_chain(nsites=50,
contact_size=10,
coupling=0.1,
onsite=1.0)
# This is to make sure that S is positive definite.
numpy.linalg.cholesky(mat_csr.todense())
# Set an identity overlap matrix.
negf.set_overlap(mat_csr)
# Initialize the system structure.
negf.init_structure(2, numpy.array([39, 49]), numpy.array([29,
39]))
# Initialize parameters relevant for the transmission.
negf.params.ec = -5.0
negf.params.emin = -0.2
negf.params.emax = 0.2
negf.params.estep = 0.005
negf.params.mu[0] = 0.1
negf.params.mu[1] = -0.1
# IMPORTANT: ni and nf must be both defined.
negf.params.ni[0] = ni
negf.params.ni[1] = nf
negf.params.nf[0] = nf
negf.params.nf[1] = ni
negf.params.kbt_t[1] = 0.01
negf.params.kbt_t[0] = 0.01
negf.params.np_real[0] = 50
negf.verbosity = 0
negf.set_params()
coupling = 0.1
negf.set_diagonal_elph_dephasing(numpy.array([coupling] * 30))
negf.solve_landauer()
tmp_currents = negf.currents()
assert tmp_currents[0] == pytest.approx(-tmp_currents[1], 1e-9)
currents.append(tmp_currents[0])
assert currents[0] == pytest.approx(-currents[1], 1e-9)
def test_density_linear_chain_neq_2d():
"""
Test the density matrix calculation at non-equilibrium for a linear
chain in full-band.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_square_2d_lattice(
nblocks=20, block_size=5, n_contact_blocks=2, coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(
2,
numpy.array([89, 99]),
numpy.array([79, 89]))
# Set parameters relevant for the density matrix calculation.
# We fully occupy all band and use mostly default values for
# the integration contour.
negf.params.ec = -5.0
negf.params.mu[0] = 0.1
negf.params.mu[1] = -0.1
negf.params.kbt_dm = (.001, .001)
negf.params.g_spin = 2.0
# Not correctly initialized, setting explicitely.
negf.params.np_real = tuple([50] * 11)
negf.params.verbose = 0
negf.set_params()
# Calculate the density matrix.
negf.solve_density()
density_matrix = negf.density_matrix()
diagonal = density_matrix.diagonal()
# The system is ballistic, therefore we should have identical
# occupation all over the chain when checking equivalent sites.
for i in range(5):
assert diagonal[i:80:5] == pytest.approx(diagonal[i], abs=1e-4)
# The occupation should 1.
assert diagonal[0] == pytest.approx(1.0, abs=1e-3)
# We should have 2 particles (due to degeneracy) per site.
diagonal = density_matrix.diagonal()
# The contact density matrix is ignored, therefore it should be zero.
assert diagonal[80:] == pytest.approx(0.0)
def test_transmission_linear_chain():
""" Test that we can calculate the transmission for an ideal linear chain. """
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(
nsites=100, contact_size=20, coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(
2,
numpy.array([79, 99]),
numpy.array([59, 79]),
numpy.array([14, 29, 44, 59]),
numpy.array([3, 0]))
# Initialize parameters relevant for the transmission.
negf.params.g_spin = 1
negf.params.emin = -3.0
negf.params.emax = 3.0
negf.params.estep = 0.01
negf.params.mu[0] = -0.5
negf.params.mu[1] = 0.5
negf.set_params()
# negf.print_tnegf()
# Set also some local DOS intervals.
negf.set_ldos_intervals(numpy.array([0, 30, 0]), numpy.array([59, 59, 29]))
negf.solve_landauer()
# Get transmission, dos and energies as numpy object
energies = negf.energies()
transmission = negf.transmission()
ldos = negf.ldos()
# The system is homogeneous, therefore the first LDOS should be equal to
# the sum of the second and third.
assert ldos[0, :] == pytest.approx(ldos[1, :] + ldos[2, :])
# Check ldos shape.
_check_ldos_shape(ldos, energies)
# The current in ballistic current units should be equal the
# spin degeneracy we set, i.e. 1
currents = negf.currents()
currents[0] == pytest.approx(1.0)
# Check that the transmission has the right integer values.
_check_transmission_values(transmission, energies)
def test_density_linear_chain_neq_bias():
"""
Test the density matrix calculation at non-equilibrium for a linear
chain in full-band.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(
nsites=100, contact_size=20, coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(
2,
numpy.array([79, 99]),
numpy.array([59, 79]))
# Set parameters relevant for the density matrix calculation.
# We fully occupy all band and use mostly default values for
# the integration contour.
negf.params.ec = -2.5
negf.params.mu[0] = 0.1
negf.params.mu[1] = -0.1
negf.params.kbt_dm = (.001, .001)
negf.params.g_spin = 2.0
negf.params.np_real[0] = 50
negf.params.verbose = 0
negf.set_params()
# Calculate the density matrix.
negf.solve_density()
density_matrix = negf.density_matrix()
diagonal = density_matrix.diagonal()
# The system is ballistic, therefore we should have identical
# occupation all over the chain.
assert diagonal[:60] == pytest.approx(diagonal[0], abs=1e-4)
# The occupation should 1.
assert diagonal[0] == pytest.approx(1.0, abs=1e-4)
# We should have 2 particles (due to degeneracy) per site.
diagonal = density_matrix.diagonal()
# The contact density matrix is ignored, therefore it should be zero.
assert diagonal[60:] == pytest.approx(0.0)
def test_transmission_automatic_partition_2d():
"""
Test that we can calculate the transmission for a 2d hamiltonian.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_square_2d_lattice(
nblocks=20, block_size=5, n_contact_blocks=2, coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(
2,
numpy.array([89, 99]),
numpy.array([79, 89]))
# Initialize parameters relevant for the transmission.
negf.params.g_spin = 1
negf.params.emin = -5.0
negf.params.emax = 5.0
negf.params.estep = 0.01
negf.params.mu[0] = 0.05
negf.params.mu[0] = -0.05
negf.set_params()
# negf.print_tnegf()
# Set also some local DOS intervals.
negf.set_ldos_intervals(numpy.array([0, 30, 0]), numpy.array([59, 59, 29]))
negf.solve_landauer()
# Get transmission, dos and energies as numpy object
transmission = negf.transmission()
ldos = negf.ldos()
# The system is homogeneous, therefore the first LDOS should be equal to
# the sum of the second and third.
assert ldos[0, :] == pytest.approx(ldos[1, :] + ldos[2, :])
# The current in ballistic current units should be equal the
# spin degeneracy we set times 5 (number of bands) times delta_mu, i.e. 0.5
currents = negf.currents()
currents[0] == pytest.approx(0.5)
# Check that the transmission peaks at 5.0.
assert numpy.max(transmission[0, :]) == pytest.approx(5.0)
def _density_linear_chain_dephasing(coupling=None, orthogonal=True):
"""
Utility to calculate the density matrix in presence of diagonal
dephasing for a nearest neighbor linear chain.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(nsites=50,
contact_size=10,
coupling=1.0)
if orthogonal:
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(50)
else:
negf.set_hamiltonian(mat_csr)
mat_csr = utils.orthogonal_linear_chain(nsites=50,
contact_size=10,
coupling=0.1,
onsite=1.0)
# This is to make sure that S is positive definite.
numpy.linalg.cholesky(mat_csr.todense())
# Set an identity overlap matrix.
negf.set_overlap(mat_csr)
# Initialize the system structure.
negf.init_structure(2, numpy.array([39, 49]), numpy.array([29, 39]))
# Initialize parameters relevant for the density matrix calculation.
negf.params.ec = -3.5
negf.params.mu[0] = -0.1
negf.params.mu[1] = 0.1
negf.params.kbt_dm[0] = 0.001
negf.params.kbt_dm[1] = 0.001
negf.params.np_real[0] = 50
negf.params.verbose = 100
negf.set_params()
if coupling is not None:
negf.set_diagonal_elph_dephasing(numpy.array([coupling] * 30))
negf.solve_density()
# Get the density matrix.
density_matrix = negf.density_matrix()
return density_matrix
def test_density_linear_chain_eq():
"""
Test the density matrix calculation at equilibrium for a linear
chain in full-band.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(
nsites=100, contact_size=20, coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(
2,
numpy.array([79, 99]),
numpy.array([59, 79]))
# Set parameters relevant for the density matrix calculation.
# We fully occupy all band and use mostly default values for
# the integration contour.
negf.params.ec = -2.5
negf.params.mu[0] = 0.0
negf.params.mu[1] = 0.0
negf.params.kbt_dm = (.001, .001)
negf.params.g_spin = 2.0
# Not correctly initialized, setting explicitely.
negf.params.np_real = tuple([0] * 11)
negf.params.verbose = 0
negf.set_params()
# Calculate the density matrix.
negf.solve_density()
density_matrix = negf.density_matrix()
# We should have 1 particles (2 degeneracy, half band occupied) per site.
diagonal = density_matrix.diagonal()
assert diagonal[:60] == pytest.approx(1.0)
# The contact density matrix is ignored, therefore it should be zero.
assert diagonal[60:] == pytest.approx(0.0)
def _transmission_linear_chain_dephasing(coupling=None):
"""
Utility to calculate the transmission in presence of diagonal
dephasing for a nearest neighbor linear chain.
"""
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat_csr = utils.orthogonal_linear_chain(nsites=100,
contact_size=10,
coupling=1.0)
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure.
negf.init_structure(2, numpy.array([89, 99]), numpy.array([79, 89]))
# Initialize parameters relevant for the transmission.
negf.params.g_spin = 1
negf.params.emin = -2.5
negf.params.emax = 2.5
negf.params.estep = 0.025
negf.params.mu[0] = 2.1
negf.params.mu[1] = -2.1
negf.verbosity = 0
negf.set_params()
if coupling is not None:
negf.set_diagonal_elph_dephasing(numpy.array([coupling] * 80))
negf.solve_landauer()
# Get transmission, dos and energies as numpy object
energies = negf.energies()
if coupling is None:
transmission = negf.transmission()
else:
transmission = negf.energy_current()
return energies, transmission
def transmission_linear_chain():
"""
Calculate the transmission for a linear chain model hamiltonian.
"""
# Start an instance of the library.
negf = pynegf.PyNegf()
# Build the sparse hamiltonian for the nearest-neighbor linear chain.
mat = numpy.zeros(shape=(100, 100), dtype='complex128')
for ii in range(80):
mat[ii, ii - 1] = 1.0
mat[ii - 1, ii] = 1.0
for ii in range(81, 100):
mat[ii, ii - 1] = 1.0
mat[ii - 1, ii] = 1.0
mat[0, 80] = 1.0
mat[80, 0] = 1.0
mat_csr = scipy.sparse.csr_matrix(mat)
mat_csr.sort_indices()
# Pass the hamiltonian to libnegf.
negf.set_hamiltonian(mat_csr)
# Set an identity overlap matrix.
negf.set_identity_overlap(100)
# Initialize the system structure. Here we specify the following
# parameters:
# number of contact: 2
# start-end index of first contact: numpy.array([80, 100])
# start-end index of second contact: numpy.array([60, 80])
# end-index of each layer, for the iterative algorithm: numpy.array([15, 30, 45, 60])
# index of bloks interacting with the contact: numpy.array([4, 1])
negf.init_structure(
2,
numpy.array([80, 100]),
numpy.array([60, 80]),
numpy.array([15, 30, 45, 60]),
numpy.array([4, 1]))
# Initialize parameters relevant for the transmission.
# the chemical potential mu is used for evaluating the current only.
negf.params.emin = -3.0
negf.params.emax = 3.0
negf.params.estep = 0.01
negf.params.mu[0] = 0.1
negf.set_params()
negf.print_tnegf()
# Set also some local DOS intervals.
negf.set_ldos_intervals(numpy.array([1, 31, 1]), numpy.array([60, 60, 30]))
negf.solve_landauer()
# Get transmission, dos and energies as numpy object.
energies = negf.energies()
print('energies', energies)
trans = negf.transmission()
ldos = negf.ldos()
currents = negf.currents()
print('Currents',currents)
print('trans', trans)