Dear everyone:
we know that enegy gap in Landau levels is hw, then we can know the
magnitude of magnatic field by claculating the gap between landau levels, in
this code, the magnitude of magnetic field I set is way different by
calculating the energy gap in Landau levels in this code, Ihave no idea what
went wrong, so I'll be thankful if you can konw what is wrong in this code.
Thank you
Following is my code—-————————————————-
### Import modules ###
import kwant
import numpy as np
from math import pi
from matplotlib import pyplot as plt
import csv
import scipy.sparse.linalg as sla
a = 1
# Lattice constant, in nm
h = 4.14e-15
# Plank's constnt in unit of eV*s
hbar = 6.58e-16
# In unit of eV*s
m = 9.11e-31
# Mass of electron in kg
q = 1.6e-19
# Charge of an electron in coulomb
t = hbar*hbar/(2*m*a*a)
# t = hbar^2/(2m(a^2))
B = 3
# Magnitude of external magnetic field, in unit of Tesla
phi0 = 4.14e-15
# Magnetic quantum
def setup_system(W=100, L=100):
### Define a function about hopping ###
def hopping(hop):
x1, y1 = hop[0].pos
# Get the position imformation of site_1
x2, y2 = hop[1].pos
# Get the position imformation of site_2
delta_x = (x2 - x1) * 1e-9
# Differance of x coordinate in nanometer
y_bar = (y1 + y2) / 2 * 1e-9
# Averge of y coordinate in nanometer
return delta_x, y_bar
### Define the shape of the system ###
def rectangle(pos):
x, y = pos
return x > -W and x < W and y > -L and y < L
### Define the shape of the lead ###
def lead_shape(pos):
x, y = pos
return (-L < y < L)
### Set up the system ###
sys = kwant.Builder()
# Builde up the system
lat = kwant.lattice.square(a, norbs = 1) # Set
up the lattice in shape of square
sys[lat.shape(rectangle, (0, 0))] = 4 * t #
Define the on-site energy
for hopx in kwant.builder.HoppingKind((1, 0), lat)(sys): #
Define the hopping in x-direction
delta_x, y_bar = hopping(hopx)
phase = 2* pi /phi0 *B *delta_x *y_bar # Phase
differnce due to magnetic field
sys[hopx] = -t * np.exp( phase*1j)
for hopy in kwant.builder.HoppingKind((0, 1), lat)(sys): #
Define the hopping in y-direction
sys[hopy] = -t
### Set up the left lead ###
lead0 = kwant.Builder(kwant.TranslationalSymmetry((-1, 0))) # The
current goes from the left lead
lead0[lat.shape(lead_shape, (0, 0))] = 4 * t #
Define the on-site energy
for hopx in kwant.builder.HoppingKind((1, 0), lat)(lead0):
# Define the hopping in x-direction
delta_x, y_bar = hopping(hopx)
phase = 2* pi /phi0 *B *delta_x *y_bar # Phase
differnce due to magnetic field
lead0[hopx] = -t * np.exp( phase*1j)
for hopy in kwant.builder.HoppingKind((0, 1), lat)(lead0): #
Define the hopping in y-direction
lead0[hopy] = -t
### Set up the right lead ###
lead1 = kwant.Builder(kwant.TranslationalSymmetry((1, 0))) # The
current goes from the left lead
lead1[lat.shape(lead_shape, (0, 0))] = 4 * t #
Define the on-site energy
for hopx in kwant.builder.HoppingKind((1, 0), lat)(lead1): #
Define the hopping in x-direction
delta_x, y_bar = hopping(hopx)
phase = 2* pi /phi0 *B *delta_x *y_bar # Phase
differnce due to magnetic field
lead1[hopx] = -t * np.exp( phase*1j)
for hopy in kwant.builder.HoppingKind((0, 1), lat)(lead1): #
Define the hopping in y-direction
lead1[hopy] = -t
### Attach the left lead and the right lead ###
sys.attach_lead(lead0)
sys.attach_lead(lead1)
### Finalize the system ###
sys = sys.finalized()
### Finally, return the system ###
return sys
sys = setup_system()
### Compute, plot and store the bandstructure ###
def plot_bandstructure(flead, momenta):
bands = kwant.physics.Bands(flead)
energies = [bands(k)[0: 10] for k in momenta]
bandenergy = []
'''np.savetxt("Momentatest_l.csv", momenta, delimiter = ",")
for i in range(1000):
bandenergy.append(energies[i])
np.savetxt("Band_energytest1_l.csv", bandenergy, delimiter = ",")'''
plt.figure(figsize=(6, 8))
plt.plot(momenta, energies, color='k')
plt.xlabel("momentum [a^-1]")
plt.ylabel("energy [eV]")
plt.ylim(0, 0.03)
plt.xlim(-1, 1)
plt.show()
#kwant.plotter.bands(sys.leads[0])
momenta = np.linspace(-1, 1, 1000)
plot_bandstructure(sys.leads[0], momenta)
plot_bandstructure(sys.leads[1], momenta)
