H.U = u
mixer.clear()
# AFM case first
success = H.read_density(
'clar-goblet.nc') # Try reading, if we already have density on file
if not success:
H.n = n_AFM.copy()
dn = H.converge(density.calc_n_insulator, tol=1e-10, mixer=mixer)
eAFM = H.Etot
H.write_density('clar-goblet.nc')
n_AFM = H.n.copy()
if u == 3.5:
p = plot.SpinPolarization(H, colorbar=True, vmax=0.4, vmin=-0.4)
p.savefig('spin_pol_U%i_AFM.pdf' % (H.U * 1000))
# Now FM case
H.q[0] += 1 # change to two more up-electrons than down
H.q[1] -= 1
success = H.read_density(
'clar-goblet.nc') # Try reading, if we already have density on file
if not success:
H.random_density()
H.set_polarization(up=[6, 28])
mixer.clear()
dn = H.converge(density.calc_n_insulator, tol=1e-10, mixer=mixer)
eFM = H.Etot
H.write_density('clar-goblet.nc')
p = plot.BondHoppings(H_mol, annotate=False, off_diagonal_only=False, cmap_e='winter')
p.legend()
p.savefig('bondHoppings.pdf')
H = HubbardHamiltonian(H_mol, U=3.5)
H.read_density('mol-ref/density.nc')
H.iterate(density.calc_n_insulator)
p = plot.Charge(H, ext_geom=molecule, colorbar=True)
p.savefig('chg.pdf')
p = plot.ChargeDifference(H, ext_geom=molecule, colorbar=True)
p.savefig('chgdiff.pdf')
p = plot.SpinPolarization(H, ext_geom=molecule, colorbar=True, vmax=0.2)
p.annotate()
p.savefig('pol.pdf')
H.H.shift(-H.find_midgap())
ev, evec = H.eigh(eigvals_only=False, spin=0)
p = plot.Wavefunction(H, 500 * evec[:, 10], ext_geom=molecule, colorbar=True)
p.savefig('wf.pdf')
p = plot.Spectrum(H)
p.savefig('spectrum.pdf')
p = plot.DOSmap(H)
p.savefig('2Ddos_map.pdf')
# 3NN tight-binding model
Hsp2 = sp2(mol, t1=2.7, t2=0.2, t3=.18)
H = HubbardHamiltonian(Hsp2)
# Plot the single-particle TB (U = 0.0) wavefunction (SO) for Type 1
H.U = 0.0
ev, evec = H.eigh(eigvals_only=False, spin=0)
N = H.q[0]
midgap = H.find_midgap()
ev -= midgap
f = 3800
v = evec[:, int(round(N)) - 1]
j = np.argmax(abs(v))
wf = f * v**2 * np.sign(v[j]) * np.sign(v)
p = plot.Wavefunction(H, wf)
p.set_title(r'$E = %.3f$ eV' % (ev[int(round(N)) - 1]))
p.savefig('Fig3_SOMO.pdf')
# Plot MFH spin polarization for U = 3.5 eV
H.U = 3.5
success = H.read_density(
'fig3_type1.nc') # Try reading, if we already have density on file
if not success:
H.set_polarization([23])
mixer = sisl.mixing.PulayMixer(0.7, history=7)
H.converge(density.calc_n_insulator, mixer=mixer)
H.write_density('fig3_type1.nc')
p = plot.SpinPolarization(H, ext_geom=mol, vmax=0.20)
p.savefig('fig3_pol.pdf')
TBham = sisl.Hamiltonian(g, spin='polarized')
for ia in g:
ib = g.close(ia, R=[0, 1.42 + 0.1])
io_a = g.a2o(ia, all=True)
for iib in ib[1]:
io_b = g.a2o(iib, all=True)
TBham[io_a[0], io_b[0]] = -2.7
# HubbardHamiltonian object and converge
HH = HubbardHamiltonian(TBham, U=None, nkpt=[100, 1, 1])
HH.set_polarization([0], dn=[g.a2o(13)])
HH.converge(density.calc_n, print_info=True, tol=1e-10, steps=3)
# Print spin-densities difference compared to sing-orbital case
print(
'\n ** Difference between spin densities for single and multi-orbital cases **'
)
print(HH.n[:, idx] - n_single)
# Add second set of bands for the multi orbital case
p.add_bands(HH, c='--r')
p.savefig('bands.pdf')
# Plot charge for multi-orbital case
p = plot.Charge(HH, vmin=0.9, vmax=1.1, colorbar=True)
p.savefig('charge.pdf')
# Plot spin polarization for multi-orbital case
p = plot.SpinPolarization(HH, vmax=0.2, vmin=-0.2, colorbar=True)
p.savefig('spinpol.pdf')
# Hubbard Hamiltonian of elecs
MFH_elec = HubbardHamiltonian(H_elec, U=U, nkpt=[102, 1, 1], kT=kT)
# Initial densities
success = MFH_elec.read_density('elec_density.nc')
if not success:
# If no densities saved, start with random densities with maximized polarization at the edges
MFH_elec.random_density()
MFH_elec.set_polarization([0], dn=[9])
# Converge Electrode Hamiltonians
dn = MFH_elec.converge(density.calc_n, mixer=mixer)
# Write also densities for future calculations
MFH_elec.write_density('elec_density.nc')
# Plot spin polarization of electrodes
p = plot.SpinPolarization(MFH_elec, colorbar=True)
p.savefig('spin_elecs.pdf')
# Find Fermi level of reservoirs and write to netcdf file
Ef_elecs = MFH_elec.fermi_level(q=MFH_elec.q)
MFH_elec.H.shift(-Ef_elecs)
MFH_elec.H.write('MFH_elec.nc')
# Build central region TB Hamiltonian
HC = H_elec.tile(16, axis=0)
HC = HC.remove([67, 68, 69, 72, 73, 74, 77, 78, 79, 82, 83, 84, 87, 88, 89])
HC.set_nsc([1, 1, 1])
HC.geometry.write('device.xyz')
# Map electrodes in the device region
elec_indx = [range(len(H_elec)), range(len(HC.H) - len(H_elec), len(HC.H))]