import sisl
from sisl import geom, Atom
import numpy as np
import os
from hubbard import HubbardHamiltonian, sp2, density, plot
W = 7
bond = 1.42
# single-orbital
g = geom.zgnr(W)
TBHam = sp2(g, t1=2.7, t2=0, t3=0)
HH = HubbardHamiltonian(TBHam, U=3, nkpt=[100, 1, 1])
HH.set_polarization([0], dn=[-1])
HH.converge(density.calc_n, print_info=True, tol=1e-10, steps=3)
n_single = HH.n * 1
# Start bands-plot, the single-orbital case will be plotted in black
p = plot.Bandstructure(HH, c='k')
class OrbitalU(sisl.Orbital):
__slots__ = ('U', )
def __init__(self, *args, U=0., **kwargs):
super().__init__(*args, **kwargs)
self.U = U
def copy(self, *args, **kwargs):
copy = super().copy(*args, **kwargs)
copy.U = self.U
f = open('FM-AFM.dat', 'w')
mixer = sisl.mixing.PulayMixer(0.7, history=7)
for u in np.arange(5, 0, -0.25):
# We approach the solutions for different U values
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()
U = 3. kT = 0.025 # Build zigzag GNR ZGNR = sisl.geom.zgnr(2) # and 3NN TB Hamiltonian H_elec = sp2(ZGNR, t1=2.7, t2=0.2, t3=0.18) # Hubbard Hamiltonian of elecs MFH_elec = HubbardHamiltonian(H_elec, U=U, nkpt=[102, 1, 1], kT=kT) # Start with random densities MFH_elec.random_density() # Converge Electrode Hamiltonians dn = MFH_elec.converge(density.calc_n, mixer=sisl.mixing.PulayMixer(weight=.7, history=7), tol=1e-10) # Central region is a repetition of the electrodes without PBC HC = H_elec.tile(3, axis=0) HC.set_nsc([1, 1, 1]) # Map electrodes in the device region elec_indx = [range(len(H_elec)), range(len(HC.H)-len(H_elec), len(HC.H))] # MFH object MFH_HC = HubbardHamiltonian(HC.H, n=np.tile(MFH_elec.n, 3), U=U, kT=kT) # First create NEGF object negf = NEGF(MFH_HC, [(MFH_elec, '-A'), (MFH_elec, '+A')], elec_indx) # Converge using Green's function method to obtain the densities dn = MFH_HC.converge(negf.calc_n_open, steps=1, mixer=sisl.mixing.PulayMixer(weight=.1), tol=0.1)
# 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')
Hsp2 = sp2(molecule)
H = HubbardHamiltonian(Hsp2, U=3.5)
H.read_density('mol-ref/density.nc')
H.iterate(density.calc_n_insulator, mixer=sisl.mixing.LinearMixer())
# Determine reference values for the tests
ev0, evec0 = H.eigh(eigvals_only=False, spin=0)
Etot0 = 1 * H.Etot
mixer = sisl.mixing.PulayMixer(0.7, history=7)
for m in [density.calc_n_insulator, density.calc_n]:
# Reset density and iterate
H.random_density()
mixer.clear()
dn = H.converge(m, tol=1e-10, steps=10, mixer=mixer, print_info=True)
ev1, evec1 = H.eigh(eigvals_only=False, spin=0)
# Total energy check:
print('Total energy difference: %.4e eV' % (Etot0 - H.Etot))
# Eigenvalues are easy to check
if np.allclose(ev1, ev0):
print('Eigenvalue check passed')
else:
# Could be that up and down spins are interchanged
print(
'Warning: Engenvalues for up-spins different. Checking down-spins instead'
)
ev1, evec1 = H.eigh(eigvals_only=False, spin=1)
if np.allclose(ev1, ev0):
# and 3NN TB Hamiltonian
H_elec = sp2(ZGNR, t1=2.7, t2=0.2, t3=0.18)
mixer = sisl.mixing.PulayMixer(0.6, history=7)
# 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])
import sisl
from hubbard import HubbardHamiltonian, sp2, density, plot
import numpy as np
import os
""" Script to benchmark the Generalized TB method of Ref. Phys. Rev. B 81, 245402 (2010) """
# Create geometry of the periodic (along x-axis) ribbon
agnr = sisl.geom.agnr(14)
zgnr = sisl.geom.zgnr(16)
lab = ['14-AGNR', '16-ZGNR']
mixer = sisl.mixing.PulayMixer(0.7, history=7)
for i, geom in enumerate([agnr, zgnr]):
# Build TB Hamiltonian, one can use the parameters from the Ref.
H0 = sp2(geom, t1=2.7, t2=0.2, t3=0.18, s1=0, s2=0, s3=0)
# Find self-consistent solution with MFH
H = HubbardHamiltonian(H0, U=2, nkpt=[100, 1, 1])
# Start with random densities
H.random_density()
mixer.clear()
dn = H.converge(density.calc_n, mixer=mixer, print_info=True)
# Plot banstructure of Hubbard Hamiltonian
p = plot.Bandstructure(H, ymax=3)
p.savefig('%s_bands.pdf'%(lab[i]))
print('\n')
# and 3NN TB Hamiltonian
H_elec = sp2(AGNR, t1=2.7, t2=0.2, t3=0.18)
mixer = sisl.mixing.PulayMixer(0.3, history=7)
# Hubbard Hamiltonian of elecs
MFH_elec = HubbardHamiltonian(H_elec, U=U, nkpt=[102, 1, 1], kT=0.025)
# Initial densities
success = MFH_elec.read_density('elec_density.nc')
if not success:
# If no densities saved, start with random densities
MFH_elec.random_density()
# 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
dist = sisl.get_distribution('fermi_dirac', smearing=kT)
Ef_elecs = MFH_elec.H.fermi_level(MFH_elec.mp, q=MFH_elec.q, distribution=dist)
MFH_elec.H.shift(-Ef_elecs)
MFH_elec.H.write('MFH_elec.nc')
# Central region is a repetition of the electrodes without PBC
HC = H_elec.tile(10, axis=0)
import sisl
"""
For this system we get an open-shell solution for U>3 eV
This test obtaines the closed-shell solution for U=2 eV for both a spin-polarized and unpolarized situation
"""
# Build sisl Geometry object
molecule = sisl.get_sile('mol-ref/mol-ref.XV').read_geometry()
molecule.sc.set_nsc([1, 1, 1])
Hsp2 = sp2(molecule)
H = HubbardHamiltonian(Hsp2, U=2.0)
H.set_polarization([36], [77])
dn = H.converge(density.calc_n_insulator,
mixer=sisl.mixing.LinearMixer(),
tol=1e-7)
print('Closed-shell spin-polarized calculation:')
print('dn: {}, Etot: {}\n'.format(dn, H.Etot))
p = plot.Plot()
for i in range(2):
ev = H.eigh(spin=i) - H.find_midgap()
ev = ev[abs(ev) < 2]
p.axes.plot(ev,
np.zeros_like(ev), ['or', 'xg'][i],
label=[r'$\sigma=\uparrow$', r'$\sigma=\downarrow$'][i])
# Compute same system with spin degeneracy
Hsp2 = sp2(molecule, spin='unpolarized')
H = HubbardHamiltonian(Hsp2, U=2.0)