# coupling to the leads - nearest neighbor only
H_scat[1, 2] = H_scat[2, 1] = H_scat[3, 4] = H_scat[4, 3] = 0.2
tcalc = TransportCalculator(
h=H_scat, # Scattering Hamiltonian
h1=H_lead, # Lead 1 (left)
h2=H_lead, # Lead 2 (right)
energies=np.arange(-3, 3, 0.02))
T_e = tcalc.get_transmission()
pylab.plot(tcalc.energies, T_e)
pylab.title('Transmission function')
pylab.show()
tcalc.set(pdos=[2, 3])
pdos_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_ne[0], ':')
pylab.plot(tcalc.energies, pdos_ne[1], '--')
pylab.title('Projected density of states')
pylab.show()
h_rot, s_rot, eps_n, vec_nn = tcalc.subdiagonalize_bfs([2, 3])
tcalc.set(h=h_rot, s=s_rot) # Set the rotated matrices
for n in range(2):
print("eigenvalue, eigenvector:", eps_n[n], ',', vec_nn[:, n])
pdos_rot_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_rot_ne[0], ':')
pylab.plot(tcalc.energies, pdos_rot_ne[1], '--')
pylab.title('Projected density of states (rotated)')
pylab.show()
def test_transport_calculator():
H_lead = np.zeros([4, 4])
# On-site energies are zero
for i in range(4):
H_lead[i, i] = 0.0
# Nearest neighbor hopping is -1.0
for i in range(3):
H_lead[i, i + 1] = -1.0
H_lead[i + 1, i] = -1.0
# Next-nearest neighbor hopping is 0.2
for i in range(2):
H_lead[i, i + 2] = 0.2
H_lead[i + 2, i] = 0.2
H_scat = np.zeros([6, 6])
# Principal layers on either side of S
H_scat[:2, :2] = H_lead[:2, :2]
H_scat[-2:, -2:] = H_lead[:2, :2]
# Scattering region
H_scat[2, 2] = 0.0
H_scat[3, 3] = 0.0
H_scat[2, 3] = -0.8
H_scat[3, 2] = -0.8
# External coupling
H_scat[1, 2] = 0.2
H_scat[2, 1] = 0.2
H_scat[3, 4] = 0.2
H_scat[4, 3] = 0.2
energies = np.arange(-3, 3, 0.02)
tcalc = TransportCalculator(h=H_scat,
h1=H_lead,
eta=0.02,
energies=energies)
T = tcalc.get_transmission()
tcalc.set(pdos=[2, 3])
pdos = tcalc.get_pdos()
tcalc.set(dos=True)
dos = tcalc.get_dos()
write('T.dat', tcalc.energies, T)
write('pdos0.dat', tcalc.energies, pdos[0])
write('pdos1.dat', tcalc.energies, pdos[1])
#subdiagonalize
h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3], apply=True)
T_rot = tcalc.get_transmission()
dos_rot = tcalc.get_dos()
pdos_rot = tcalc.get_pdos()
write('T_rot.dat', tcalc.energies, T_rot)
write('pdos0_rot.dat', tcalc.energies, pdos_rot[0])
write('pdos1_rot.dat', tcalc.energies, pdos_rot[1])
print('Subspace eigenvalues:', eps)
assert sum(abs(eps - (-0.8, 0.8))) < 2.0e-15, 'Subdiagonalization. error'
print('Max deviation of T after the rotation:', np.abs(T - T_rot).max())
assert max(abs(T - T_rot)) < 2.0e-15, 'Subdiagonalization. error'
#remove coupling
h_cut, s_cut = tcalc.cutcoupling_bfs([2], apply=True)
T_cut = tcalc.get_transmission()
dos_cut = tcalc.get_dos()
pdos_cut = tcalc.get_pdos()
write('T_cut.dat', tcalc.energies, T_cut)
write('pdos0_cut.dat', tcalc.energies, pdos_cut[0])
write('pdos1_cut.dat', tcalc.energies, pdos_cut[1])
H_scat[3, 3] = 0.0
H_scat[2, 3] = -0.8
H_scat[3, 2] = -0.8
# External coupling
H_scat[1, 2] = 0.2
H_scat[2, 1] = 0.2
H_scat[3, 4] = 0.2
H_scat[4, 3] = 0.2
energies = np.arange(-3, 3, 0.02)
tcalc = TransportCalculator(h=H_scat, h1=H_lead, eta=0.02, energies=energies)
T = tcalc.get_transmission()
tcalc.set(pdos=[2, 3])
pdos = tcalc.get_pdos()
tcalc.set(dos=True)
dos = tcalc.get_dos()
write('T.dat', tcalc.energies, T)
write('pdos0.dat', tcalc.energies, pdos[0])
write('pdos1.dat', tcalc.energies, pdos[1])
#subdiagonalize
h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3], apply=True)
T_rot = tcalc.get_transmission()
dos_rot = tcalc.get_dos()
pdos_rot = tcalc.get_pdos()
write('T_rot.dat', tcalc.energies, T_rot)
for n in range(len(eps_n)):
print("bf %i corresponds to the eigenvalue %.2f eV" % (bfs[n], eps_n[n]))
# Switch to the rotated basis set
tcalc.set(h=h_rot, s=s_rot)
# plot the transmission function
tcalc.set(energies=np.arange(-8, 4, 0.1))
T = tcalc.get_transmission()
pylab.plot(tcalc.energies, T)
pylab.title('Transmission function')
pylab.show()
# ... and the projected density of states (pdos) of the H2 molecular orbitals
tcalc.set(pdos=bfs)
pdos_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_ne[0], label='bonding')
pylab.plot(tcalc.energies, pdos_ne[1], label='anti-bonding')
pylab.title('Projected density of states')
pylab.legend()
pylab.show()
# Cut the coupling to the anti-bonding orbital.
print('Cutting the coupling to the renormalized molecular state at %.2f eV' %
(eps_n[1]))
h_rot_cut, s_rot_cut = tcalc.cutcoupling_bfs([bfs[1]])
tcalc.set(h=h_rot_cut, s=s_rot_cut)
pylab.plot(tcalc.energies, tcalc.get_transmission())
pylab.title('Transmission without anti-bonding orbital')
pylab.show()
# coupling to the leads - nearest neighbor only
H_scat[1, 2] = H_scat[2, 1] = H_scat[3, 4] = H_scat[4, 3] = 0.2
tcalc = TransportCalculator(h=H_scat, # Scattering Hamiltonian
h1=H_lead, # Lead 1 (left)
h2=H_lead, # Lead 2 (right)
energies=np.arange(-3, 3, 0.02))
T_e = tcalc.get_transmission()
pylab.plot(tcalc.energies, T_e)
pylab.title('Transmission function')
pylab.show()
tcalc.set(pdos=[2, 3])
pdos_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_ne[0], ':')
pylab.plot(tcalc.energies, pdos_ne[1], '--')
pylab.title('Projected density of states')
pylab.show()
h_rot, s_rot, eps_n, vec_nn = tcalc.subdiagonalize_bfs([2, 3])
tcalc.set(h=h_rot, s=s_rot) # Set the rotated matrices
for n in range(2):
print("eigenvalue, eigenvector:", eps_n[n], ',', vec_nn[:, n])
pdos_rot_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_rot_ne[0], ':')
pylab.plot(tcalc.energies, pdos_rot_ne[1], '--')
pylab.title('Projected density of states (rotated)')
pylab.show()
# External coupling
H_scat[1,2] = 0.2
H_scat[2,1] = 0.2
H_scat[3,4] = 0.2
H_scat[4,3] = 0.2
energies = np.arange(-3,3,0.02)
tcalc = TransportCalculator(h=H_scat,
h1=H_lead,
h2=H_lead,
energies=energies)
T = tcalc.get_transmission()
tcalc.set(pdos=[2, 3])
pdos = tcalc.get_pdos()
tcalc.set(dos=True)
dos = tcalc.get_dos()
write('T.dat',tcalc.energies,T)
write('pdos0.dat', tcalc.energies,pdos[0])
write('pdos1.dat', tcalc.energies,pdos[1])
#subdiagonalize
h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3])
tcalc.set(h=h_rot,s=s_rot)
T_rot = tcalc.get_transmission()
dos_rot = tcalc.get_dos()
pdos_rot = tcalc.get_pdos()
for n in range(len(eps_n)):
print("bf %i corresponds to the eigenvalue %.2f eV" % (bfs[n], eps_n[n]))
# Switch to the rotated basis set
tcalc.set(h=h_rot, s=s_rot)
# plot the transmission function
tcalc.set(energies=np.arange(-8, 4, 0.1))
T = tcalc.get_transmission()
pylab.plot(tcalc.energies, T)
pylab.title('Transmission function')
pylab.show()
# ... and the projected density of states (pdos) of the H2 molecular orbitals
tcalc.set(pdos=bfs)
pdos_ne = tcalc.get_pdos()
pylab.plot(tcalc.energies, pdos_ne[0], label='bonding')
pylab.plot(tcalc.energies, pdos_ne[1], label='anti-bonding')
pylab.title('Projected density of states')
pylab.legend()
pylab.show()
# Cut the coupling to the anti-bonding orbital.
print('Cutting the coupling to the renormalized molecular state at %.2f eV' % (
eps_n[1]))
h_rot_cut, s_rot_cut = tcalc.cutcoupling_bfs([bfs[1]])
tcalc.set(h=h_rot_cut, s=s_rot_cut)
pylab.plot(tcalc.energies, tcalc.get_transmission())
pylab.title('Transmission without anti-bonding orbital')
pylab.show()