Eig TB

eigTB solves the Tight-Binding Hamiltonian.

eigTB can:

  • set the lattice hoppings.

  • set the lattice onsite energies.

  • set hopping and onsite disorder.

  • solve the Tight-Binding Hamiltonian:

    • get eigenenergies and eigenvectors.
    • get sublattice polarizations.

  • select states using energy range or polarization condition.

Examples

Square lattice

Lattice creation:

# imports
from latticeTB import *
from eigTB import *
from plotTB import *
from math import pi
from collections import OrderedDict

# lattice
nx, ny = 5, 5
ri = [[0, 0]]
tags = [b'a']
lat = latticeTB(tags=tags, ri=ri, nor=1, ang=pi/2)
lat.get_lattice(nx=nx, ny=ny)
fig_lat = lat.plt_lattice(ms=18, plt_label=True)
_images/lat.png

Tight-Binding eigenvalue problem:

  • with nearest-neighbor hoppings

    t1 = 1.
eig = eigTB(lat)
eig.set_hop(ho=[t1])
eig.get_ham()
eig.get_eig()
plot = plotTB(eig)
fig_lat_bonds = plot.plt_lattice(ms=18)
fig_spec = plot.plt_spec()
plt.show()
# save
save = saveFigTB(sys=eig, dir_name='square', params={'t1': t1})
save.save_fig_lat(fig_lat, 'lat')
save.save_fig(fig_lat_bonds, 'lattice')
save.save_fig(fig_spec, 'spec')
    _images/lattice_t1(1+0j).png _images/spec_t1(1+0j).png

  • adding next nearest-neighbor hoppings

    t2 = .8
eig.set_hop(ho=[t1, t2])
eig.get_ham()
eig.get_eig(eigenvec=True)
plot = plotTB(eig)
zero = eig.get_states_en(-.001, .001)
fig_lat_bonds = plot.plt_lattice(ms=18)
fig_spec = plot.plt_spec()
fig_zero = plot.plt_intensity(zero)
plt.show()
# save
save = saveFigTB(sys=eig, dir_name='square', params=OrderedDict([('t1', t1), ('t2', t2)]))
save.save_fig(fig_lat_bonds, 'lattice')
save.save_fig(fig_spec, 'spec')
save.save_fig(fig_zero, 'zero_mode')
    _images/lattice_t1(1+0j)_t2(0,8+0j).png _images/spec_t1(1+0j)_t2(0,8+0j).png

    The next-neighbors hoppings lead to a mode of zero energy.

    _images/zero_mode_t1(1+0j)_t2(0,8+0j).png

  • adding next next nearest-neighbor hoppings

    t3 = .6
eig.set_hop(ho=[t1, t2, t3])
eig.get_ham()
eig.get_eig()
plot = plotTB(eig)
fig_lat_bonds = plot.plt_lattice(ms=18)
fig_spec = plot.plt_spec()
plt.show()
# save
save = saveFigTB(sys=eig, dir_name='square', params=OrderedDict([('t1', t1), ('t2', t2), ('t3', t3)]))
save.save_fig(fig_lat_bonds, 'lattice')
save.save_fig(fig_spec, 'spec')
    _images/lattice_t1(1+0j)_t2(0,8+0j)_t3(0,6+0j).png _images/spec_t1(1+0j)_t2(0,8+0j)_t3(0,6+0j).png

  • adding next next next nearest-neighbor hoppings

    t4 = .4
eig.set_hop(ho=[t1, t2, t3, t4])
eig.get_ham()
eig.get_eig()
plot = plotTB(eig)
fig_lat_bonds = plot.plt_lattice(ms=18)
fig_spec = plot.plt_spec()
plt.show()
# save
save = saveFigTB(sys=eig, dir_name='square', params=OrderedDict([('t1', t1), ('t2', t2), ('t3', t3), ('t4', t4)]))
save.save_fig(fig_lat_bonds, 'lattice')
save.save_fig(fig_spec, 'spec')
    _images/lattice_t1(1+0j)_t2(0,8+0j)_t3(0,6+0j)_t4(0,4+0j).png _images/spec_t1(1+0j)_t2(0,8+0j)_t3(0,6+0j)_t4(0,4+0j).png

Feedback

Please send comments or suggestions for improvement to cpoli83 at hotmail dot fr