def test_bulk_silicon():
a_si = 5.50
PRIMITIVE_CELL = [[0, 0.5 * a_si, 0.5 * a_si], [0.5 * a_si, 0, 0.5 * a_si],
[0.5 * a_si, 0.5 * a_si, 0]]
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S'}
xyz_file = """2
Si2 cell
Si1 0.0000000000 0.0000000000 0.0000000000
Si2 1.3750000000 1.3750000000 1.3750000000
"""
h = tb.Hamiltonian(xyz=xyz_file, nn_distance=2.5)
h.initialize()
h.set_periodic_bc(PRIMITIVE_CELL)
sym_points = ['L', 'GAMMA', 'X']
num_points = [10, 25]
k = tb.get_k_coords(sym_points, num_points, 'Si')
band_sructure = []
vals = np.zeros((sum(num_points), h.h_matrix.shape[0]), dtype=np.complex)
for jj, item in enumerate(k):
vals[jj, :], _ = h.diagonalize_periodic_bc(item)
band_structure = np.real(np.array(vals))
np.testing.assert_allclose(band_structure,
expected_bulk_silicon_band_structure(),
atol=1e-4)
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 get_h_matrix(path):
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
hamiltonian = tb.Hamiltonian(xyz=path, nn_distance=2.4)
hamiltonian.initialize()
a_si = 5.50
PRIMITIVE_CELL = [[0, 0, a_si]]
hamiltonian.set_periodic_bc(PRIMITIVE_CELL)
return hamiltonian.h_matrix
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 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 compute_tb_matrices(save=True):
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
h = tb.Hamiltonian(xyz='/home/mk/TB_project/input_samples/SiNW2.xyz', nn_distance=2.4)
h.initialize()
period = [0, 0, 5.50]
h.set_periodic_bc([period])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
coords = h.get_site_coordinates()
if save:
np.save('h_l', h_l)
np.save('h_0', h_0)
np.save('h_r', h_r)
np.save('coords', coords)
return h_l, h_0, h_r, coords
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 compute_tb_matrices(input_file, save=save_to):
"""
The script computes or load TB matrices from the disk.
:param input_file: xyz-file for atomic system
:param save: if is not None, save TB matrices into the directory specified by the parameter save
:return: h_l, h_0, h_r, coords, path
"""
if os.path.isdir(input_file):
h_l = np.load(os.path.join(input_file, 'h_l.npy'))
h_0 = np.load(os.path.join(input_file, 'h_0.npy'))
h_r = np.load(os.path.join(input_file, 'h_r.npy'))
coords = np.load(os.path.join(input_file, 'coords.npy'))
path = input_file
else:
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
h = tb.Hamiltonian(xyz=input_file, nn_distance=2.4)
h.initialize()
period = [0, 0, 5.50]
h.set_periodic_bc([period])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
coords = h.get_site_coordinates()
if save:
sys_name = os.path.basename(input_file) # get the base name
sys_name = os.path.splitext(sys_name)[0] # get rid of the extension
path = os.path.join(save, sys_name)
shutil.copy2(input_file, path)
np.save(os.path.join(path, 'h_l'), h_l)
np.save(os.path.join(path, 'h_0'), h_0)
np.save(os.path.join(path, 'h_r'), h_r)
np.save(os.path.join(path, 'coords'), coords)
else:
path = None
return h_l, h_0, h_r, coords, path
def bs(path='c:\users\sammy\desktop\NanoNet\input_samples', kk=0, flag=True):
"""
This function computes the band gap / band structure for Silicon Nanowire
:param path: directory path to where xyz input files are stored
:param flag: boolean statements
:return: band gap / band structure
"""
# define orbitals sets
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
band_gaps = []
band_structures = []
for xyz_file in os.listdir(path):
if xyz_file.endswith('xyz'):
widths = [s for s in xyz_file if s.isdigit()]
width = int(''.join(widths))
print(width)
hamiltonian = tb.Hamiltonian(xyz=os.path.join(path, xyz_file),
nn_distance=2.4)
hamiltonian.initialize()
if flag:
plt.axis('off')
plt.imshow(np.log(np.abs(hamiltonian.h_matrix)))
plt.savefig('hamiltonian.pdf')
plt.show()
a_si = 5.50
PRIMITIVE_CELL = [[0, 0, a_si]]
hamiltonian.set_periodic_bc(PRIMITIVE_CELL)
num_points = len(kk)
band_structure = []
for jj in xrange(num_points):
print(jj)
vals, _ = hamiltonian.diagonalize_periodic_bc([0, 0, kk[jj]])
band_structure.append(vals)
band_structure = np.array(band_structure)
band_structures.append(band_structure)
cba = band_structure.copy()
vba = band_structure.copy()
cba[cba < 0] = 1000
vba[vba > 0] = -1000
band_gap = np.min(cba) - np.max(vba)
band_gaps.append(band_gap)
if flag:
fig1, ax1 = plt.subplots()
ax1.axes.set_xlim(0.0, 0.5)
#ax1.axes.set_ylim(0.00, -0.04)
ax1.axes.set_ylim(-0.3, 0.0)
ax1.plot(kk, np.sort(np.real(vba)))
ax1.set_xlabel(r'Wave vector ($\frac{\pi}{a}$)')
ax1.set_ylabel(r'Energy (eV)')
ax1.set_title('Valence band, NW width={} u.c.'.format(width))
fig1.tight_layout()
plt.savefig('bs_vb.pdf')
fig2, ax2 = plt.subplots()
ax1.axes.set_xlim(0.0, 0.5)
#ax2.axes.set_ylim(0.0, 0.06)
ax2.axes.set_ylim(2.0, 2.5)
ax2.plot(kk, np.sort(np.real(cba)))
ax2.set_xlabel(r'Wave vector ($\frac{\pi}{a}$)')
ax2.set_ylabel(r'Energy (eV)')
ax2.set_title(
'Conduction band, NW width={} u.c.'.format(width))
fig2.tight_layout()
plt.savefig('bs_cb.pdf')
return band_gaps, band_structures
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)
def inverse_bs_problem():
import sys
sys.path.insert(0, '/home/mk/TB_project/tb')
import 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_C_C={'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 = """6
# H cell
# A1 0.0000000000 0.0000000000 0.0000000000
# B2 0.0000000000 0.0000000000 1.0000000000
# C3 0.0000000000 0.0000000000 2.0000000000
# A4 0.0000000000 1.0000000000 0.0000000000
# B5 0.0000000000 1.0000000000 1.0000000000
# C6 0.0000000000 1.0000000000 2.0000000000
# """
#
# h = tb.Hamiltonian(xyz=xyz_file, nn_distance=1.1)
# h.initialize()
# h.set_periodic_bc([[0, 0, 3.0]])
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
h = tb.Hamiltonian(xyz='/home/mk/TB_project/input_samples/SiNW.xyz',
nn_distance=2.4)
h.initialize()
h.set_periodic_bc([[0, 0, 5.50]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
# energy = np.linspace(2.13, 2.15, 20)
# energy = np.linspace(-2.1, 1.0, 50)
energy = np.linspace(2.05, 2.5, 200)
# energy = np.linspace(2.07, 2.3, 50) + 0.2
# energy = np.linspace(2.3950, 2.4050, 20)
# energy = energy[20:]
eigs = []
for E in energy:
print(E)
vals, vects = surface_greens_function_poles(E, h_l, h_0, h_r)
vals = np.diag(vals)
vals.setflags(write=1)
for j, v in enumerate(vals):
if np.abs(np.absolute(v) - 1.0) > 0.01:
vals[j] = float('nan')
else:
vals[j] = np.angle(v)
print("The element number is", j, vals[j])
eigs.append(vals)
plt.plot(energy, np.array(eigs), 'o')
plt.show()
def main1():
import sys
sys.path.insert(0, '/home/mk/TB_project/tb')
import tb
tb.Atom.orbital_sets = {'Si': 'SiliconSP3D5S', 'H': 'HydrogenS'}
h = tb.Hamiltonian(xyz='/home/mk/NEGF_project/SiNW.xyz', nn_distance=2.4)
h.initialize()
h.set_periodic_bc([[0, 0, 5.50]])
h_l, h_0, h_r = h.get_coupling_hamiltonians()
# energy = np.linspace(2.07, 2.3, 50)
# energy = np.linspace(2.07, 2.3, 50) + 0.2
# energy = np.linspace(-1.0, -0.3, 200)
energy = np.concatenate((np.linspace(-0.8, -0.3,
100), np.linspace(2.05, 2.5, 100)))
# energy = np.linspace(2.3950, 2.4050, 20)
# energy = energy[20:35]
sgf_l = []
sgf_r = []
factor = []
factor1 = []
factor2 = []
num_sites = h_0.shape[0]
for j, E in enumerate(energy):
# L, R = surface_greens_function_poles_Shur(j, E, h_l, h_0, h_r)
L, R, _, _, _ = surface_greens_function(E, h_l, h_0, h_r)
test_gf = E * np.identity(num_sites) - h_0 - L - R
metrics = np.linalg.cond(test_gf)
print("{} of {}: energy is {}, metrics is {}".format(
j + 1, energy.shape[0], E, metrics))
# if metrics > 15000:
# R = iterate_gf(E, h_0, h_l, h_r, R, 1)
# L = iterate_gf(E, h_0, h_l, h_r, L, 1)
sgf_l.append(L)
sgf_r.append(R)
# factor.append(phase)
# factor1.append(phase1)
# factor2.append(phase2)
sgf_l = np.array(sgf_l)
sgf_r = np.array(sgf_r)
factor = np.array(factor)
factor1 = np.array(factor1)
factor2 = np.array(factor2)
gf = np.linalg.pinv(
np.multiply.outer(energy, np.identity(num_sites)) - h_0 - sgf_l -
sgf_r)
# gf = regularize_gf(gf)
dos = -np.trace(np.imag(gf), axis1=1, axis2=2)
tr = np.zeros((energy.shape[0]), dtype=np.complex)
dos = 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)
dos[j] = np.real(np.trace(1j * (gf0 - gf0.H)))
tr[j] = np.real(np.trace(gamma_l * gf0 * gamma_r * gf0.H))
ax = plt.axes()
ax.set_xlabel('Energy (eV)')
ax.set_ylabel('DOS')
ax.plot(energy, dos)
plt.show()
ax = plt.axes()
ax.set_xlabel('Energy (eV)')
ax.set_ylabel('Transmission coefficient (a.u.)')
ax.plot(energy, tr)
plt.show()
plt.plot(dos)
plt.show()
print(sgf_l.shape)
