Dear developer,
I was trying to calculate the conductivity of
honeycomb lattice, where I have included the Haldane term along with the
spin-orbit Rashba term (Kane-Mele model). I was following the tutorial provided
in chapter 2.9 (https://kwant-project.org/doc/1/tutorial/kpm). The code shows
an error when I include the spin in the system. My code is attached below,
from matplotlib import pyplot as plt
import tinyarray as tn
import kwant
import numpy as np
t = 1
t2 = 0.3
sgm_0=tn.array([[1,0],[0,1]])
sgm_x=tn.array([[0,1],[1,0]])
sgm_y=tn.array([[0,-1j],[1j,0]])
sgm_z=tn.array([[1,0],[0,-1]])
def make_syst_topo(l=20, a=1, m=0):
alpha = 0.01
syst = kwant.Builder()
lat = kwant.lattice.honeycomb(a, norbs=1, name=['a', 'b'])
a = lat.a
b = lat.b
def rectangle(pos):
x, y = pos
return - l<= x <= +l and - l<= y <= +l
def rashba(site_i,site_j):
d_ij = site_i.pos - site_j.pos
return -1j*alpha*(sgm_x*d_ij[1]-sgm_y*d_ij[0])
def nn_hop(site_i, site_j):
return rashba(site_i, site_j) - t * sgm_0
syst[lat.shape(rectangle, (0, 0))] = 0.0*sgm_0
syst[kwant.builder.HoppingKind((0, 0), a, b)] = nn_hop
syst[kwant.builder.HoppingKind((0, 1), a, b)] = nn_hop
syst[kwant.builder.HoppingKind((-1, 1), a, b)] = nn_hop
syst[lat.a.neighbors()] = 1j * t2 * sgm_z
syst[lat.b.neighbors()] = -1j * t2*sgm_z
syst.eradicate_dangling()
return lat, syst.finalized()
def plot_system(syst):
kwant.plot(syst,site_size=0.1, hop_lw=0.01)
# Plot fill density of states plus curves on the same axes.
def plot_dos_and_curves(dos, labels_to_data):
plt.figure(figsize=(10,8))
plt.fill_between(dos[0], dos[1], label="DoS [a.u.]",
alpha=0.5, color='gray')
for label, (x, y) in labels_to_data:
plt.plot(x, y, label=label, linewidth=2)
plt.legend(loc='upper center', framealpha=0.5, fontsize=12)
plt.xlabel(r'$E/t$');
# plt.ylabel('ylabel')
plt.show()
plt.clf()
def conductivity_example():
# construct the Haldane model
lat, fsyst = make_syst_topo()
# find 'A' and 'B' sites in the unit cell at the center of the disk
where = lambda s: np.linalg.norm(s.pos) < 1
# component 'xx'
s_factory = kwant.kpm.LocalVectors(fsyst, where)
cond_xx = kwant.kpm.conductivity(fsyst, alpha='x', beta='x', mean=True,
num_vectors=None, vector_factory=s_factory)
# component 'xx'
s_factory = kwant.kpm.LocalVectors(fsyst, where)
cond_yy = kwant.kpm.conductivity(fsyst, alpha='y', beta='y', mean=True,
num_vectors=None, vector_factory=s_factory)
# component 'xy'
s_factory = kwant.kpm.LocalVectors(fsyst, where)
cond_xy = kwant.kpm.conductivity(fsyst, alpha='x', beta='y', mean=True,
num_vectors=None, vector_factory=s_factory)
energies_x = cond_xx.energies
energies_y = cond_yy.energies
cond_array_xx = np.array([cond_xx(e, temperature=0.00) for e in energies_x])
cond_array_xy = np.array([cond_xy(e, temperature=0.00) for e in energies_x])
cond_array_yy = np.array([cond_yy(e, temperature=0.00) for e in energies_y])
# area of the unit cell per site
area_per_site = np.abs(np.cross(*lat.prim_vecs)) / len(lat.sublattices)
cond_array_xx /= area_per_site
cond_array_xy /= area_per_site
cond_array_yy /= area_per_site
# ldos
s_factory = kwant.kpm.LocalVectors(fsyst, where)
spectrum = kwant.kpm.SpectralDensity(fsyst, num_vectors=None,
vector_factory=s_factory)
plot_dos_and_curves(
(spectrum.energies, spectrum.densities * 8),
[
(r'$\sigma_{xx} / 4$',
(energies_x, cond_array_xx / 4)),
(r'$\sigma_{xy}$',
(energies_x, cond_array_xy)),
(r'$\sigma_{yy} / 4$',
(energies_y, cond_array_yy / 4))]
)
def main():
fsyst = make_syst_topo()[1]
plot_system(fsyst)
conductivity_example()
if __name__ == '__main__':
main()
I shall look forward to your kind reply.
