def test_atomic_chain_two_kinds_of_atoms():
site_energy1 = -1.0
site_energy2 = -2.0
coupling = -1.0
l_const = 2.0
a = tb.Atom('A')
a.add_orbital(
title='s',
energy=site_energy1,
)
b = tb.Atom('B')
b.add_orbital(
title='s',
energy=site_energy2,
)
tb.Atom.orbital_sets = {'A': a, 'B': b}
xyz_file = """2
H cell
A 0.0000000000 0.0000000000 0.0000000000
B 0.0000000000 0.0000000000 1.0000000000
"""
tb.set_tb_params(PARAMS_A_B={'ss_sigma': coupling})
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
h.initialize()
assert (h.is_hermitian(), True)
PRIMITIVE_CELL = [[0, 0, l_const]]
h.set_periodic_bc(PRIMITIVE_CELL)
num_points = 10
kk = np.linspace(0, 3.14 / 2, num_points, endpoint=True)
band_structure = []
for jj in range(num_points):
vals, _ = h.diagonalize_periodic_bc([0.0, 0.0, kk[jj]])
band_structure.append(vals)
band_structure = np.array(band_structure)
desired_value = np.zeros(band_structure.shape)
b = site_energy1 + site_energy2
c = site_energy1 * site_energy2 - (2.0 * coupling *
np.cos(0.5 * kk * l_const))**2
desired_value[:, 0] = 0.5 * (b - np.sqrt(b**2 - 4.0 * c))
desired_value[:, 1] = 0.5 * (b + np.sqrt(b**2 - 4.0 * c))
np.testing.assert_allclose(band_structure, desired_value, atol=1e-9)
def main3():
import sys
sys.path.insert(0, '/home/mk/TB_project/tb')
import tb
a = tb.Atom('A')
a.add_orbital('s', -0.7)
tb.Atom.orbital_sets = {'A': a}
tb.set_tb_params(PARAMS_A_A={'ss_sigma': -0.5},
PARAMS_B_B={'ss_sigma': -0.5},
PARAMS_A_B={'ss_sigma': -0.5},
PARAMS_B_C={'ss_sigma': -0.5},
PARAMS_A_C={'ss_sigma': -0.5})
xyz_file = """1
H cell
A1 0.0000000000 0.0000000000 0.0000000000
"""
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=2.1)
h.initialize()
h.set_periodic_bc([[0, 0, 1.0]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
energy = np.linspace(-3.0, 1.5, 700)
sgf_l = []
sgf_r = []
for E in energy:
L, R, _, _, _ = surface_greens_function(E, h_l, h_0, h_r)
# L, R = surface_greens_function_poles_Shur(E, h_l, h_0, h_r)
sgf_l.append(L)
sgf_r.append(R)
sgf_l = np.array(sgf_l)
sgf_r = np.array(sgf_r)
num_sites = h_0.shape[0]
gf = np.linalg.pinv(
np.multiply.outer(energy, np.identity(num_sites)) - h_0 - sgf_l -
sgf_r)
dos = -np.trace(np.imag(gf), axis1=1, axis2=2)
tr = np.zeros((energy.shape[0]), dtype=np.complex)
for j, E in enumerate(energy):
gf0 = np.matrix(gf[j, :, :])
gamma_l = 1j * (np.matrix(sgf_l[j, :, :]) -
np.matrix(sgf_l[j, :, :]).H)
gamma_r = 1j * (np.matrix(sgf_r[j, :, :]) -
np.matrix(sgf_r[j, :, :]).H)
tr[j] = np.real(np.trace(gamma_l * gf0 * gamma_r * gf0.H))
dos[j] = np.real(np.trace(1j * (gf0 - gf0.H)))
print(sgf_l.shape)
def single_atom_chain():
"""
Test set for a single-atom chain.
:return:
"""
sys.path.insert(0, '/home/mk/TB_project/tb')
a = tb.Atom('A')
a.add_orbital('s', 0.7)
tb.Atom.orbital_sets = {'A': a}
tb.set_tb_params(PARAMS_A_A={'ss_sigma': 0.5})
xyz_file = """1
H cell
A1 0.0000000000 0.0000000000 0.0000000000
"""
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
h.initialize()
h.set_periodic_bc([[0, 0, 1.0]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
num_sites = h_0.shape[0]
energy = np.linspace(-3.0, 3.0, 300)
tr = np.zeros((energy.shape[0]))
dos = np.zeros((energy.shape[0]))
sgf_l = []
sgf_r = []
for j, E in enumerate(energy):
se_l, se_r = tb.surface_greens_function(E, h_l, h_0, h_r)
sgf_l.append(se_l)
sgf_r.append(se_r)
gf = np.linalg.pinv(E * np.identity(num_sites) - h_0 - se_l - se_r)
gf = np.matrix(gf)
gamma_l = 1j * (np.matrix(se_l) - np.matrix(se_l).H)
gamma_r = 1j * (np.matrix(se_r) - np.matrix(se_r).H)
tr[j] = np.real(np.trace(gamma_l * gf * gamma_r * gf.H))
dos[j] = np.real(np.trace(1j * (gf - gf.H)))
sgf_l = np.array(sgf_l)
sgf_r = np.array(sgf_r)
return energy, dos, tr, h, sgf_l, sgf_r
def test_gf_single_atom_chain():
sys.path.insert(0, '/home/mk/TB_project/tb')
a = tb.Atom('A')
a.add_orbital('s', 0.7)
tb.Atom.orbital_sets = {'A': a}
tb.set_tb_params(PARAMS_A_A={'ss_sigma': 0.5})
xyz_file = """1
H cell
A1 0.0000000000 0.0000000000 0.0000000000
"""
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
h.initialize()
h.set_periodic_bc([[0, 0, 1.0]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
energy = np.linspace(-3.0, 3.0, 300)
sgf_l = []
sgf_r = []
for E in energy:
L, R = tb.surface_greens_function(E, h_l, h_0, h_r)
sgf_l.append(L)
sgf_r.append(R)
sgf_l = np.array(sgf_l)
sgf_r = np.array(sgf_r)
num_sites = h_0.shape[0]
gf = np.linalg.pinv(
np.multiply.outer(energy, np.identity(num_sites)) - h_0 - sgf_l -
sgf_r)
np.testing.assert_allclose(sgf_l, sgf_r, atol=1e-5)
expected = h_l * simple_chain_greens_function(energy, h_0, h_r) * h_r
np.testing.assert_allclose(np.squeeze(sgf_r),
np.squeeze(expected),
atol=1e-5)
def test_simple_atomic_chain():
site_energy = -1.0
coupling = -1.0
l_const = 1.0
a = tb.Atom('A')
a.add_orbital(
title='s',
energy=-1,
)
tb.Atom.orbital_sets = {'A': a}
xyz_file = """1
H cell
A 0.0000000000 0.0000000000 0.0000000000
"""
tb.set_tb_params(PARAMS_A_A={'ss_sigma': -1.0})
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
h.initialize()
assert (h.is_hermitian(), True)
PRIMITIVE_CELL = [[0, 0, l_const]]
h.set_periodic_bc(PRIMITIVE_CELL)
num_points = 10
kk = np.linspace(0, 3.14 / l_const, num_points, endpoint=True)
band_structure = []
for jj in range(num_points):
vals, _ = h.diagonalize_periodic_bc([0.0, 0.0, kk[jj]])
band_structure.append(vals)
band_structure = np.array(band_structure)
desired_value = site_energy + 2 * coupling * np.cos(l_const * kk)
np.testing.assert_allclose(band_structure,
desired_value[:, np.newaxis],
atol=1e-9)
def test_gf_complex_chain():
sys.path.insert(0, '/home/mk/TB_project/tb')
a = tb.Atom('A')
a.add_orbital('s', -0.7)
b = tb.Atom('B')
b.add_orbital('s', -0.5)
c = tb.Atom('C')
c.add_orbital('s', -0.3)
tb.Atom.orbital_sets = {'A': a, 'B': b, 'C': c}
tb.set_tb_params(PARAMS_A_A={'ss_sigma': -0.5},
PARAMS_B_B={'ss_sigma': -0.5},
PARAMS_A_B={'ss_sigma': -0.5},
PARAMS_B_C={'ss_sigma': -0.5},
PARAMS_A_C={'ss_sigma': -0.5})
xyz_file = """4
H cell
A1 0.0000000000 0.0000000000 0.0000000000
B2 0.0000000000 0.0000000000 1.0000000000
A2 0.0000000000 1.0000000000 0.0000000000
B3 0.0000000000 1.0000000000 1.0000000000
"""
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
h.initialize()
h.set_periodic_bc([[0, 0, 2.0]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
energy = np.linspace(-3.0, 1.5, 700)
sgf_l = []
sgf_r = []
for E in energy:
L, R = tb.surface_greens_function(E, h_l, h_0, h_r)
sgf_l.append(L)
sgf_r.append(R)
sgf_l = np.array(sgf_l)
sgf_r = np.array(sgf_r)
num_sites = h_0.shape[0]
gf = np.linalg.pinv(
np.multiply.outer(energy, np.identity(num_sites)) - h_0 - sgf_l -
sgf_r)
tr = np.zeros((energy.shape[0]))
dos = np.zeros((energy.shape[0]))
for j, E in enumerate(energy):
gf0 = np.matrix(gf[j, :, :])
gamma_l = 1j * (np.matrix(sgf_l[j, :, :]) -
np.matrix(sgf_l[j, :, :]).H)
gamma_r = 1j * (np.matrix(sgf_r[j, :, :]) -
np.matrix(sgf_r[j, :, :]).H)
tr[j] = np.real(np.trace(gamma_l * gf0 * gamma_r * gf0.H))
dos[j] = np.real(np.trace(1j * (gf0 - gf0.H)))
np.testing.assert_allclose(dos, expected_dos_of_complex_chain(), atol=1e-5)
np.testing.assert_allclose(tr, expected_tr_of_complex_chain(), atol=1e-5)
