def __init__(self, Ed, Ep, tpd, tpp, tppp):
self.Ed = Ed
self.Ep = Ep
self.tpd = tpd
self.tpp = tpp
self.tppp = tppp
dim_k = 2
dim_r = 2
lat = [(1,0), (0,1)]
orb = [(0,0), (.5,0), (0,.5)]
self.icorr_orbs = [0] # list of indices of correlated orbitals
# composition: has-a relationship with tb_model
self.model = ptb.tb_model(dim_k, dim_r, lat, orb)
self.model.set_onsite([Ed,Ep,Ep])
# (amplitude, i, j, [latt. vector to cell containing j])
hoppings = [
( tpd, 0, 1, (0,0)), # p-d hoppings
(-tpd, 0, 2, (0,0)),
(-tpd, 0, 1, (-1,0)),
( tpd, 0, 2, (0,-1)),
(-tpp, 1, 2, (0,0)), # diagonal p-p hoppings
(-tpp, 1, 2, (1,-1)),
( tpp, 1, 2, (1,0)),
( tpp, 1, 2, (0,-1)),
( tppp,1, 1, (1,0)), # tpp'
( tppp,2, 2, (0,1)),
]
for amp,i,j,lat in hoppings:
self.model.set_hop(amp, i, j, lat)
def HaldanePTB(delta,t1,hop2,phi):
# define lattice vectors
lat=[[1.0,0.0],[0.5,np.sqrt(3.0)/2.0]]
# define coordinates of orbitals
orb=[[1./3.,1./3.],[2./3.,2./3.]]
# make two dimensional tight-binding Haldane model
haldane=ptb.tb_model(2,2,lat,orb)
# set model parameters
t2=hop2*np.exp(1.j*phi)
# set on-site energies
haldane.set_onsite([-delta,delta])
# set hoppings (one for each connected pair of orbitals)
# from j in R to i in 0
# (amplitude, i, j, [lattice vector to cell containing j])
haldane.set_hop(t1, 0, 1, [ 0, 0])
haldane.set_hop(t1, 1, 0, [ 1, 0])
haldane.set_hop(t1, 1, 0, [ 0, 1])
# add second neighbour complex hoppings
haldane.set_hop(t2 , 0, 0, [ 0, -1])
haldane.set_hop(t2 , 0, 0, [ 1, 0])
haldane.set_hop(t2 , 0, 0, [ -1, 1])
haldane.set_hop(t2 , 1, 1, [ -1, 0])
haldane.set_hop(t2 , 1, 1, [ 1,-1])
haldane.set_hop(t2 , 1, 1, [ 0, 1])
return haldane
def test_1d(dt=0.0,t=1):
E0=0.0
mymodel=pythtb.tb_model(dim_k=3,dim_r=3,lat=np.eye(3),orb=[[0,0,0],[0,0,0.1]])
mymodel.set_onsite(-E0,0)
mymodel.set_onsite(E0,1)
mymodel.set_hop(-t-dt,0,1,[0,0,0])
mymodel.set_hop(-t+dt,1,0,[0,0,1])
zs=np.arange(-1,1,0.01)
#zs=[0.0]
kpoints= [[0,0,x] for x in zs]
evals=mymodel.solve_all(kpoints)
#for i in range(evals.shape[0]):
# plt.plot(zs,evals[i,:])
myanatb=anatb(mymodel,kpts=kpoints)
myanatb.plot_COHP_fatband(k_x=zs)
return
#wks=np.abs(myanatb.get_cohp_block_pair([0],[1]))
#wks=myanatb.get_cohp_block_pair([0],[1])
wks=myanatb.get_cohp_all_pair()
wks=np.moveaxis(wks,0,-1)
kslist=zs*2
ekslist=evals
wkslist=wks
print(wks)
axis=plot_band_weight(kslist,ekslist,wkslist=wks,efermi=None,yrange=None,output=None,style='color',color='blue',axis=None,width=10,xticks=None)
axis.set_xlabel('k ($\pi/a$)')
plt.show()
def model1d(ep,ed,tzp,tzd,l1,l1z,l3,mp=1000.,md1=1000.,md2=1000.,tdiagp=0.,tdiagd1=0.,tdiagd2=0.,txy=0.,txydiag=0.,X=0.,Xz=0.,l1plane=0.,l1diag=0.,lWeyl=0.,l3plane1=0.,l3plane2=0.,l3xy=0.,l3x2y2=0.,kx=0.,ky=0.): my_model=tb_model(dim_r=1,dim_k=1,lat=[[1.0]],orb=[[0.],[0.],[0.]],nspin=2) ### diagonal terms #(1+kx^2+ky^2) my_model.set_onsite([ep,ed,ed]) my_model.set_onsite([(kx**2+ky**2)/(2*mp),kx**2/md1+ky**2/md2,kx**2/md2+ky**2/md1],mode="add") #(1+kx^2+ky^2)\cos kz my_model.set_hop(tzp,0,0,[1.]) my_model.set_hop(tdiagp*(kx**2+ky**2),0,0,[1.],mode="add") my_model.set_hop(tzd,1,1,[1.]) my_model.set_hop(tdiagd1*(kx**2)+tdiagd2*(ky**2),1,1,[1.],mode="add") my_model.set_hop(tzd,2,2,[1.]) my_model.set_hop(tdiagd2*(kx**2)+tdiagd1*(ky**2),2,2,[1.],mode="add") ### dxz dyz terms #kx ky my_model.set_hop(txy*kx*ky,1,2,[0.]) my_model.set_hop(txydiag*kx*ky,1,2,[1.],mode="add") my_model.set_hop(txydiag*kx*ky,1,2,[-1.],mode="add") #\sigma_z (1+kx^2+ky^2)(1+\cos kz) my_model.set_hop([0.,0.,0., (l1+l1plane*(kx**2+ky**2))*1.0j], 1, 2, [0.],mode="add") my_model.set_hop([0.,0.,0., (l1z+l1diag*(kx**2+ky**2))*1.0j], 1, 2, [1.],mode="add") my_model.set_hop([0.,0.,0., (l1z+l1diag*(kx**2+ky**2))*1.0j], 1, 2, [-1.],mode="add") #(\sigma_x kx +\sigma_y ky)\sin kz my_model.set_hop([0., lWeyl*kx*1.0j, lWeyl*ky*1.0j,0.],1,2,[1.],mode="add") my_model.set_hop([0.,-lWeyl*kx*1.0j,-lWeyl*ky*1.0j,0.],1,2,[-1.],mode="add") ### pz (dyz,dxz) terms #(kx,ky)(1+\cos kz) my_model.set_hop(X*ky*1.0j,0,1,[0.]) my_model.set_hop(Xz*ky*1.0j,0,1,[1.],mode="add") my_model.set_hop(Xz*ky*1.0j,0,1,[-1.],mode="add") my_model.set_hop(X *kx*1.0j,0,2,[0.]) my_model.set_hop(Xz*kx*1.0j,0,2,[1.],mode="add") my_model.set_hop(Xz*kx*1.0j,0,2,[-1.],mode="add") #\sigma_z(kx,ky)(1+\cos kz) my_model.set_hop([0.,0.,0., X*kx*1.0j],0,1,[0.],mode="add") my_model.set_hop([0.,0.,0., Xz*kx*1.0j],0,1,[1.],mode="add") my_model.set_hop([0.,0.,0., Xz*kx*1.0j],0,1,[-1.],mode="add") my_model.set_hop([0.,0.,0.,- X*ky*1.0j],0,2,[0.],mode="add") my_model.set_hop([0.,0.,0.,-Xz*ky*1.0j],0,2,[1.],mode="add") my_model.set_hop([0.,0.,0.,-Xz*ky*1.0j],0,2,[-1.],mode="add") #(\sigma_x,y)\sin kz my_model.set_hop([0., l3*1.0j,0.,0.],0,1,[1.],mode="add") my_model.set_hop([0.,-l3*1.0j,0.,0.],0,1,[-1.],mode="add") my_model.set_hop([0.,0.,-l3*1.0j,0.],0,2,[1.],mode="add") my_model.set_hop([0.,0., l3*1.0j,0.],0,2,[-1.],mode="add") my_model.set_hop([0., (l3plane1*kx**2+l3plane2*ky**2)*1.0j,0.,0.],0,1,[1.],mode="add") my_model.set_hop([0.,-(l3plane1*kx**2+l3plane2*ky**2)*1.0j,0.,0.],0,1,[-1.],mode="add") my_model.set_hop([0.,0.,-(l3plane2*kx**2+l3plane1*ky**2)*1.0j,0.],0,2,[1.],mode="add") my_model.set_hop([0.,0., (l3plane2*kx**2+l3plane1*ky**2)*1.0j,0.],0,2,[-1.],mode="add") #kx ky and kx2-ky2 my_model.set_hop([0., l3x2y2*(kx**2-ky**2)*1.0j,-l3xy*kx*ky*1.0j,0.],0,1,[1.],mode="add") my_model.set_hop([0.,-l3x2y2*(kx**2-ky**2)*1.0j, l3xy*kx*ky*1.0j,0.],0,1,[1.],mode="add") my_model.set_hop([0., l3xy*kx*ky*1.0j, l3x2y2*(kx**2-ky**2)*1.0j,0.],0,2,[1.],mode="add") my_model.set_hop([0.,-l3xy*kx*ky*1.0j,-l3x2y2*(kx**2-ky**2)*1.0j,0.],0,2,[1.],mode="add") return my_model
def test_TB_from_pythTB(self):
try:
from pythtb import tb_model
except (ModuleNotFoundError):
print(
'skipping pythTB test because module pythTB could not be imported'
)
return
# set up simple 1band model with NN and NNN hopping
n_orb = 3
lattice = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
orbitals = [[0, 0, 0]] * n_orb
d0 = 1.0
t0 = -0.5
ptb = tb_model(3, 3, lattice, orbitals)
# set cfs and hoppings
ptb.set_onsite([d0] * n_orb)
ptb.set_hop(1 * t0, 0, 0, [1, 0, 0])
ptb.set_hop(2 * t0, 1, 1, [1, 0, 0])
ptb.set_hop(1 * t0, 0, 0, [0, 1, 0])
ptb.set_hop(4 * t0, 2, 2, [0, 1, 0])
ptb.set_hop(1 * t0, 1, 1, [0, 0, 1])
ptb.set_hop(8 * t0, 2, 2, [0, 0, 1])
tbl_ptb = TB_from_pythTB(ptb)
# Check that hopping dict matches pythtb model above
hr_0 = tbl_ptb.hoppings[(0, 0, 0)]
self.assertTrue(hr_0[0, 0] == hr_0[1, 1] == hr_0[2, 2] == d0)
hr_100 = tbl_ptb.hoppings[(1, 0, 0)]
self.assertTrue(2 * hr_100[0, 0] == hr_100[1, 1] == 2 * t0)
hr_010 = tbl_ptb.hoppings[(0, 1, 0)]
self.assertTrue(4 * hr_010[0, 0] == hr_010[2, 2] == 4 * t0)
hr_001 = tbl_ptb.hoppings[(0, 0, 1)]
self.assertTrue(8 * hr_001[1, 1] == hr_001[2, 2] == 8 * t0)
# Evaluate dispersion on k-space path
Gamma = np.array([0.0, 0.0, 0.0])
M = np.array([0.5, 0.5, 0.0])
paths = [(Gamma, M)]
kvecs, dist = k_space_path(paths, num=101, bz=tbl_ptb.bz)
epsilon_k = tbl_ptb.dispersion(kvecs)
self.assertTrue(epsilon_k.shape == (101, 3))
# Obtain H_k on same path and compare eigenvalues against dispersion
H_k = tbl_ptb.fourier(kvecs)
evals = np.linalg.eigvalsh(H_k)
self.assertTrue(np.allclose(evals, epsilon_k))
# Obtain H_k as Gf
H_k = tbl_ptb.fourier(tbl_ptb.get_kmesh(11))
self.assertTrue(H_k.data.shape == (1331, 3, 3))
def _set_up_tb_model(self):
self.num_el = self.num_atoms - self.charge
if not self.relax_multiplicity:
if self.multiplicity % 2 == self.num_el % 2:
raise Exception(
"ERROR: Charge & multiplicity combination not allowed!")
# determine spin populations
self.num_spin_el = [
(self.num_el + (self.multiplicity - 1)) // 2,
(self.num_el - (self.multiplicity - 1)) // 2,
]
else:
self.num_spin_el = [0, 0]
lat = [[1.0, 0.0], [0.0, 1.0]]
orb = []
for at in self.ase_geom:
orb.append(at.position[:2])
self.model_a = pythtb.tb_model(0, 2, lat, orb, nspin=1)
self.model_b = pythtb.tb_model(0, 2, lat, orb, nspin=1)
for i_at in range(len(self.neighbors)):
for d in range(len(self.t_list)):
t = self.t_list[d]
if t == 0.0:
continue
ns = self.neighbors[i_at][d]
for n in ns:
if n < i_at:
self.model_a.set_hop(-t, i_at, n)
self.model_b.set_hop(-t, i_at, n)
def test_compare_pythtb():
pt_model = pt.tb_model(1, 1, lat=[[1]], orb=[[0], [0.2]])
tb_model = tb.Model(dim=1, pos=[[0], [0.2]], uc=[[1]])
pt_model.set_hop(3j, 0, 1, [1])
tb_model.add_hop(3j, 0, 1, [1])
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0])).all()
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0], convention=1)).all()
assert np.isclose(pt_model._gen_ham([1]), tb_model.hamilton([1], convention=1)).all()
assert np.isclose(pt_model._gen_ham([0.2]), tb_model.hamilton(0.2, convention=1)).all()
def __init__(self,
dim_k,
dim_r,
lat,
orb,
basis_set=None,
per=None,
nspin=2,
nel=None,
width=0.2,
verbose=True):
#mytb.__init__(self,dim_k,dim_r,lat,orb,per=per,nspin=nspin,nel=nel,width=width,verbose=True)
self._basis_set = basis_set
self._dim_k = dim_k
self._dim_r = dim_r
self._norb = len(orb)
self._tbmodel = tb_model(dim_k, dim_r, lat, orb, per=per, nspin=nspin)
self._tbmodel0 = None
self._eigenvals = None
self._eigenvecs = None
self._nspin = nspin
self._nstate = self._norb * self._nspin
# if fix_spin: _efermi is a tuple (ef_up,ef_dn)
self._efermi = None
self._occupations = None
self._kpts = None
# _kweight is a array [w1,w2,....].
self._kweights = None
self._nel = nel
self._U = None
self._width = width
self._verbose = verbose
self._eps = 0.001
self._onsite_en = np.zeros(len(orb))
self._nbar = np.ndarray([len(orb), 2])
#self._fix_spin=fix_spin
# U function index r,p,q,s include spin index or not.
self._U_spin_indexed = None
self._old_occupations = None
self._occupations = None
# self._rho: density matrix _nstate*_nstate
self._rho = None #np.zeros((self._norb*self._nspin ,self._norb*self._nspin))
self._total_energy = None
self._niter = 0
def test_compare_pythtb():
"""
Compare a tight-binding model against a PythTB reference, using convention 1.
"""
pt_model = pt.tb_model(1, 1, lat=[[1]], orb=[[0], [0.2]])
tb_model = tb.Model(dim=1, pos=[[0], [0.2]], uc=[[1]])
pt_model.set_hop(3j, 0, 1, [1])
tb_model.add_hop(3j, 0, 1, [1])
# pylint: disable=protected-access
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0])).all()
assert np.isclose(pt_model._gen_ham([0]),
tb_model.hamilton([0], convention=1)).all()
assert np.isclose(pt_model._gen_ham([1]),
tb_model.hamilton([1], convention=1)).all()
assert np.isclose(pt_model._gen_ham([0.2]),
tb_model.hamilton(0.2, convention=1)).all()
def __init__(self, crystal):
""" Create instance of the Tight binding model
:type crystal: crystal object
:param crystal: a crystal object containing atoms
"""
self.crystal = crystal
self.crystal.brillouinZone.band_model = "Tight Binding"
self.spg = (crystal.lattice, crystal.getAtomPositons(),
crystal.getAtomNumbers())
self._orbital_positons = []
for atom in crystal.atoms:
for orbital in atom.orbitals:
self._orbital_positons.append(atom.position)
self.setGrid()
self.model = tb.tb_model(3, 3, self.crystal.lattice,
self._orbital_positons)
def __init__(self, crystal):
""" Create instance of the Parabolic Band model
:type crystal: crystal object
:param crystal: a crystal object containing atoms
"""
self._crystal = crystal
self._crystal.brillouinzone.band_model = "Parabolic"
self._spg = (crystal.lattice, crystal.get_atom_positons(),
crystal.get_atom_numbers())
self._orbital_positons = []
for atom in crystal.atoms:
for orbital in atom.orbitals:
self._orbital_positons.append(atom.position)
self.set_grid()
self._model = tb.tb_model(3, 3, self._crystal.lattice,
self._orbital_positons)
def make_model(self):
if self.primitive_atoms is not None:
atoms = self.primitive_atoms
else:
atoms = self.atoms
lat = atoms.get_cell()
apos = atoms.get_scaled_positions()
masses = atoms.get_masses()
orb = []
for pos in apos:
for i in range(3):
orb.append(pos)
model = pythtb.tb_model(3, 3, lat=lat, orb=orb)
atom_positions = atoms.get_positions()
for ifce in self.ifc:
#print ifce
iatom = ifce['iatom']
jatom = ifce['jatom']
jpos = ifce['jpos']
R0 = atom_positions[ifce['jatom'] - 1]
dis = R0 - jpos
#print self.atoms.get_cell()
R = np.linalg.solve(atoms.get_cell(), dis)
#print R
R = [int(round(x)) for x in R]
#print R
for a in range(3):
for b in range(3):
i = 3 * (iatom - 1) + a
j = 3 * (jatom - 1) + b
val = ifce['ifc'][a, b] * Hartree / np.sqrt(
masses[iatom - 1] * masses[jatom - 1])
#print i,j,R
if iatom == jatom and a == b and R == [0, 0, 0]:
model.set_onsite(val * 2, ind_i=i)
else:
model.set_hop(val, i, j, R, allow_conjugate_pair=True)
#print self.atoms.get_positions()
self.model = model
def pythtb_Haldane():
lat=[[1.0,0.0],[0.5,np.sqrt(3.0)/2.0]]
orb=[[1./3.,1./3.],[2./3.,2./3.]]
my_model=pythtb.tb_model(2,2,lat,orb)
delta=0.2
t=-1.0
t2 =0.15*np.exp((1.j)*np.pi/2.)
t2c=t2.conjugate()
my_model.set_onsite([-delta,delta])
my_model.set_hop(t, 0, 1, [ 0, 0])
my_model.set_hop(t, 1, 0, [ 1, 0])
my_model.set_hop(t, 1, 0, [ 0, 1])
my_model.set_hop(t2 , 0, 0, [ 1, 0])
my_model.set_hop(t2 , 1, 1, [ 1,-1])
my_model.set_hop(t2 , 1, 1, [ 0, 1])
my_model.set_hop(t2c, 1, 1, [ 1, 0])
my_model.set_hop(t2c, 0, 0, [ 1,-1])
my_model.set_hop(t2c, 0, 0, [ 0, 1])
return my_model
# by Sinisa Coh and David Vanderbilt (see gpl-pythtb.txt) #from pythtb import * # import TB model class import pythtb as tb # import TB model class import numpy as np import matplotlib.pyplot as plt #parameter############################################ # information used for title, figure name. info = ['triangular lattice model', 'TR'] # define lattice vectors lat=[[np.sqrt(3.0)/2.0,0.5], [0.,1.]] # define coordinates of orbitals orb=[[0,0], [2./3.,-1./3.], [1./3.,1./3.]] # make two dimensional tight-binding model my_model=tb.tb_model(2,2,lat,orb) # set model parameters t1 = 1.0 t2 = 1.0/4 phi = np.pi/3 # calculate bulk or edge spectrum glue_edgs = True #glue_edgs = False # set on-site energies my_model.set_onsite([0.0]*len(orb)) ###################################################### # set hoppings (one for each connected pair of orbitals)
import numpy as np from numpy import linalg as LA #set and solve the parton band model t, td = 1., 0.5j Lx, Ly = 6, 4 L = Lx * Ly * 2 chimax = 800 cutoff = 1e-10 # define lattice vectors lat = [[2.0, 0.0], [0.0, 1.0]] # define coordinates of orbitals orb = [[0.0, 0.0], [0.5, 0.0]] # make two dimensional tight-binding model parton = tb.tb_model(2, 2, lat, orb) # set model parameters # add first neighbour hoppings parton.set_hop(t, 0, 1, [0, 0]) parton.set_hop(t, 1, 0, [1, 0]) parton.set_hop(t, 0, 0, [0, 1]) parton.set_hop(-t, 1, 1, [0, 1]) # add second neighbour hoppings parton.set_hop(td, 0, 1, [0, 1]) parton.set_hop(td, 1, 0, [0, 1]) parton.set_hop(-td, 1, 0, [1, 1]) parton.set_hop(-td, 0, 1, [-1, 1]) #We first work with a finite system # cutout finite model first along direction x without PBC tmp_parton = parton.cut_piece(Lx, 0, glue_edgs=False)
def setup_model3d(M02=-0.012,M12=-3.8,M22=0.00425,M01=0.002,M11=2.4,M21=-0.006,M03=-0.002,M13=-0.2,M23=0.0001,A = -4.4*1.,B = 2.2*1.,C = 0.004*1.,X = 0.412*1.,L1=0.01,L2=0.001,L3=0.004): # define lattice vectors lat=[[1.0,0.0,0.0],[0.0,0.1,0.0],[0.0,0.0,0.1]] # define coordinates of orbitals orb=[[0.5,0.5,0.0],[0.0,0.0,0.0],[0.0,0.0,0.0],[0.0,0.0,0.0]] # make three dimensional tight-binding model my_model=tb_model(3,3,lat,orb,[0,1,2],2) # set model parameters # M01 = 0.04*1. # M11 = 2.4*1. # M21 = -0.2*1. # M02 = 0. # M12 = -3.8*1. # M22 = 0.14*1. # M03 = -0.002*-4. # M13 = -0.2*1. # M23 = 0.002*1. # A = -4.4*1. # B = 2.2*1. # C = 0.004*1. # X = 0.412*1. # L1 = 0.0105*1.0*scalefactor1 # L2 = 0.003*1.0*scalefactor2 # L3 = 0.019*1.0*scalefactor3 # Lsymbr = 0.000001 #LR = 0.005*0. #onsite my_model.set_onsite([M01+4.0*M11+2.0*M21,M02+4.0*M12+2.0*M22,M02+4.0*M12+2.0*M22,M03+4.0*M13+2.0*M23], mode ="reset") #my_model.set_onsite([0.,0.,0.,0.]) # set hoppings (one for each connected pair of orbitals) # (amplitude, i, j, [lattice vector to cell containing j]) #pz to pz my_model.set_hop(-M11, 0, 0, [ 1, 0, 0], mode ="reset") my_model.set_hop(-M11, 0, 0, [ 0, 1, 0], mode ="reset") my_model.set_hop(-M21, 0, 0, [ 0, 0, 1], mode ="reset") #dyz to dyz my_model.set_hop(-M12-B, 1, 1, [ 1, 0, 0], mode ="reset") my_model.set_hop(-M12+B, 1, 1, [ 0, 1, 0], mode ="reset") my_model.set_hop(-M22, 1, 1, [ 0, 0, 1], mode ="reset") #dxz to dxz my_model.set_hop(-M12+B, 2, 2, [ 1, 0, 0], mode ="reset") my_model.set_hop(-M12-B, 2, 2, [ 0, 1, 0], mode ="reset") my_model.set_hop(-M22, 2, 2, [ 0, 0, 1], mode ="reset") #dxy to dxy my_model.set_hop(-M13, 3, 3, [ 1, 0, 0], mode ="reset") my_model.set_hop(-M13, 3, 3, [ 0, 1, 0], mode ="reset") my_model.set_hop(-M23, 3, 3, [ 0, 0, 1], mode ="reset") #pz to dyz #n.b. to check the sign of the following term : hopping integral from orbital 1 at lattice [0,1,0] to orbital 0 at origin, and -ie^ikz +hc ~ 2sinkz my_model.set_hop(X/2.0, 0, 1, [ 0, -1, 0], mode ="reset") my_model.set_hop(-X/2.0, 0, 1, [ 0, 1, 0], mode ="reset") #pz to dxz my_model.set_hop(X/2.0, 0, 2, [ -1, 0, 0], mode ="reset") my_model.set_hop(-X/2.0, 0, 2, [ 1, 0, 0], mode ="reset") #dyz to dxz my_model.set_hop(-A/4.0, 1, 2, [ 1, 1, 0], mode ="reset") my_model.set_hop(-A/4.0, 1, 2, [-1,-1, 0], mode ="reset") my_model.set_hop( A/4.0, 1, 2, [ 1,-1, 0], mode ="reset") my_model.set_hop( A/4.0, 1, 2, [-1, 1, 0], mode ="reset") ##check these two terms #dyz to dxy my_model.set_hop(-C/4.0, 1, 3, [ 1, 0, 1], mode ="reset") my_model.set_hop(-C/4.0, 1, 3, [-1, 0,-1], mode ="reset") my_model.set_hop( C/4.0, 1, 3, [ 1, 0,-1], mode ="reset") my_model.set_hop( C/4.0, 1, 3, [-1, 0, 1], mode ="reset") #dxz to dxy my_model.set_hop(-C/4.0, 2, 3, [ 0, 1, 1], mode ="reset") my_model.set_hop(-C/4.0, 2, 3, [ 0,-1,-1], mode ="reset") my_model.set_hop( C/4.0, 2, 3, [ 0, 1,-1], mode ="reset") my_model.set_hop( C/4.0, 2, 3, [ 0,-1, 1], mode ="reset") # set SOC my_model.set_hop([0.,0.,0., L1*1.0j], 1, 2, [0.,0.,0.], mode="add") my_model.set_hop([0.,0.,-L2*1.0j,0.], 1, 3, [0.,0.,0.], mode="add") my_model.set_hop([0., L2*1.0j,0.,0.], 2, 3, [0.,0.,0.], mode="add") my_model.set_hop([0., L3*1.0j/2.0,0.,0.], 0, 1, [0.,0., 1.], mode="add") my_model.set_hop([0.,-L3*1.0j/2.0,0.,0.], 0, 1, [0.,0.,-1.], mode="add") my_model.set_hop([0.,0.,-L3*1.0j/2.0,0.], 0, 2, [0.,0., 1.], mode="add") my_model.set_hop([0.,0., L3*1.0j/2.0,0.], 0, 2, [0.,0.,-1.], mode="add") #set Rashba ... only implemented for x-hops now # my_model.set_hop([0.,0.,LR*1.j,0.], 0, 0, [1.,0.,0.] , mode="add") # my_model.set_hop([0.,0.,LR*1.j,0.], 1, 1, [1.,0.,0.] , mode="add") # my_model.set_hop([0.,0.,LR*1.j,0.], 2, 2, [1.,0.,0.] , mode="add") # my_model.set_hop([0.,0.,LR*1.j,0.], 3, 3, [1.,0.,0.] , mode="add") #small explicit sigma_y breaking term to separate # my_model.set_onsite([0.,0.,0.,-Lsymbr], 0, mode="add") # my_model.set_onsite([0.,0.,0.,-Lsymbr], 1, mode="add") # my_model.set_onsite([0.,0.,0.,-Lsymbr], 2, mode="add") # my_model.set_onsite([0.,0.,0.,-Lsymbr], 3, mode="add") # my_model.set_onsite([0.,0.,Lsymbr,0.], 0, mode="add") # my_model.set_onsite([0.,0.,Lsymbr,0.], 1, mode="add") # my_model.set_onsite([0.,0.,Lsymbr,0.], 2, mode="add") # my_model.set_onsite([0.,0.,Lsymbr,0.], 3, mode="add") return my_model
def setup_model3dwithevenL3(scalefactor,scalefactorhopp=1.,scalefactorhopd=1.,scalefactorgap=-5.,scalefactordxytop=1.):
# define lattice vectors
lat=[[1.0,0.0,0.0],[0.0,0.1,0.0],[0.0,0.0,0.1]]
# define coordinates of orbitals
orb=[[0.5,0.5,0.0],[0.0,0.0,0.0],[0.0,0.0,0.0],[0.0,0.0,0.0]]
# make three dimensional tight-binding model
my_model=tb_model(3,3,lat,orb,[0,1,2],2)
# set model parameters
M01 = 0.04*1.*scalefactor
M11 = 2.4*1.
M21 = -0.8*scalefactorhopp
M02 = 0.
M12 = -3.8*1.
M22 = 0.14**scalefactorhopd
M03 = -0.002*-4.*scalefactordxytop
M13 = -0.2*1.
M23 = 0.002*1.
A = -4.4*1.
B = 2.2*1.
C = 0.004*1.
X = 0.412*1.
L1 = 0.0105*1.
L2 = 0.003*1.
L3 = 0.019*scalefactorgap
#onsite
my_model.set_onsite([M01+4.0*M11+2.0*M21,M02+4.0*M12+2.0*M22,M02+4.0*M12+2.0*M22,M03+4.0*M13+2.0*M23], mode ="reset")
#my_model.set_onsite([0.,0.,0.,0.])
# set hoppings (one for each connected pair of orbitals)
# (amplitude, i, j, [lattice vector to cell containing j])
#pz to pz
my_model.set_hop(-M11, 0, 0, [ 1, 0, 0], mode ="reset")
my_model.set_hop(-M11, 0, 0, [ 0, 1, 0], mode ="reset")
my_model.set_hop(-M21, 0, 0, [ 0, 0, 1], mode ="reset")
#dyz to dyz
my_model.set_hop(-M12-B, 1, 1, [ 1, 0, 0], mode ="reset")
my_model.set_hop(-M12+B, 1, 1, [ 0, 1, 0], mode ="reset")
my_model.set_hop(-M22, 1, 1, [ 0, 0, 1], mode ="reset")
#dxz to dxz
my_model.set_hop(-M12+B, 2, 2, [ 1, 0, 0], mode ="reset")
my_model.set_hop(-M12-B, 2, 2, [ 0, 1, 0], mode ="reset")
my_model.set_hop(-M22, 2, 2, [ 0, 0, 1], mode ="reset")
#dxy to dxy
my_model.set_hop(-M13, 3, 3, [ 1, 0, 0], mode ="reset")
my_model.set_hop(-M13, 3, 3, [ 0, 1, 0], mode ="reset")
my_model.set_hop(-M23, 3, 3, [ 0, 0, 1], mode ="reset")
#pz to dyz
#n.b. to check the sign of the following term : hopping integral from orbital 1 at lattice [0,1,0] to orbital 0 at origin, and -ie^ikz +hc ~ 2sinkz
my_model.set_hop(X/2.0, 0, 1, [ 0, -1, 0], mode ="reset")
my_model.set_hop(-X/2.0, 0, 1, [ 0, 1, 0], mode ="reset")
#pz to dxz
my_model.set_hop(X/2.0, 0, 2, [ -1, 0, 0], mode ="reset")
my_model.set_hop(-X/2.0, 0, 2, [ 1, 0, 0], mode ="reset")
#dyz to dxz
my_model.set_hop(-A/4.0, 1, 2, [ 1, 1, 0], mode ="reset")
my_model.set_hop(-A/4.0, 1, 2, [-1,-1, 0], mode ="reset")
my_model.set_hop( A/4.0, 1, 2, [ 1,-1, 0], mode ="reset")
my_model.set_hop( A/4.0, 1, 2, [-1, 1, 0], mode ="reset")
##check these two terms
#dyz to dxy
my_model.set_hop(-C/4.0, 1, 3, [ 1, 0, 1], mode ="reset")
my_model.set_hop(-C/4.0, 1, 3, [-1, 0,-1], mode ="reset")
my_model.set_hop( C/4.0, 1, 3, [ 1, 0,-1], mode ="reset")
my_model.set_hop( C/4.0, 1, 3, [-1, 0, 1], mode ="reset")
#dxz to dxy
my_model.set_hop(-C/4.0, 2, 3, [ 0, 1, 1], mode ="reset")
my_model.set_hop(-C/4.0, 2, 3, [ 0,-1,-1], mode ="reset")
my_model.set_hop( C/4.0, 2, 3, [ 0, 1,-1], mode ="reset")
my_model.set_hop( C/4.0, 2, 3, [ 0,-1, 1], mode ="reset")
# set SOC
my_model.set_hop([0.,0.,0., L1*1.0j], 1, 2, [0.,0.,0.], mode="add")
my_model.set_hop([0.,0.,-L2*1.0j,0.], 1, 3, [0.,0.,0.], mode="add")
my_model.set_hop([0., L2*1.0j,0.,0.], 2, 3, [0.,0.,0.], mode="add")
my_model.set_hop([0., L3*1.0/2.0,0.,0.], 0, 1, [0.,0., 1.], mode="add")
my_model.set_hop([0., L3*1.0/2.0,0.,0.], 0, 1, [0.,0.,-1.], mode="add")
my_model.set_hop([0.,0., L3*1.0/2.0,0.], 0, 2, [0.,0., 1.], mode="add")
my_model.set_hop([0.,0., L3*1.0/2.0,0.], 0, 2, [0.,0.,-1.], mode="add")
return my_model
import numpy as np
import pythtb as ptb
import matplotlib.pyplot as plt
import time
import wannierberri as wb
SYM=wb.symmetry
# Example for the interface PythTB-WannierBerri. Extracted from
# http://www.physics.rutgers.edu/~dhv/pythtb-book-examples/ptb_samples.html
# 3D model of Li on bcc lattice, with s orbitals only
# define lattice vectors
lat=[[-0.5, 0.5, 0.5],[ 0.5,-0.5, 0.5],[ 0.5, 0.5,-0.5]]
# define coordinates of orbitals
orb=[[0.0,0.0,0.0]]
# make 3D model
my_model=ptb.tb_model(3,3,lat,orb)
# set model parameters
# lattice parameter implicitly set to a=1
Es= 4.5 # site energy
t =-1.4 # hopping parameter
# set on-site energy
my_model.set_onsite([Es])
# set hoppings along four unique bonds
# note that neighboring cell must be specified in lattice coordinates
for R in ([1,0,0],[0,1,0],[0,0,1],[1,1,1]):
my_model.set_hop(t, 0, 0, R)
system=wb.System_PythTB(my_model,berry=True)
# by Sinisa Coh and David Vanderbilt (see gpl-pythtb.txt) #from pythtb import * # import TB model class import pythtb as tb # import TB model class import numpy as np import matplotlib.pyplot as plt #parameter############################################ # information used for title, figure name. info = ['triangular lattice model', 'TR'] # define lattice vectors lat = [[np.sqrt(3.0) / 2.0, 0.5], [0., 1.]] # define coordinates of orbitals orb = [[0, 0], [2. / 3., -1. / 3.], [1. / 3., 1. / 3.]] # make two dimensional tight-binding model my_model = tb.tb_model(2, 2, lat, orb) # set model parameters t1 = 1.0 t2 = 1.0 / 4 phi = np.pi / 3 # calculate bulk or edge spectrum glue_edgs = True #glue_edgs = False # set on-site energies my_model.set_onsite([0.0] * len(orb)) ###################################################### # set hoppings (one for each connected pair of orbitals)
