Hi Kwant Users !
I was trying to plot the band structure of the SSH model using
kwant.continuum. I could do it when the hopping terms are constant. Now let
say the hoppings are linearly varying along x direction (t*x) or say I want
to add a chemical potential like (\mu*x). In that case, how should I
introduce this potential in the code ?
I have attached my code below. It will be a great help if anyone kindly
tells me where I need to modify the code and how to insert this (\mu*x
term) in the code.
The code is attached herewith.
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import kwant
import kwant.continuum
import scipy.sparse.linalg
import scipy.linalg
import numpy as np
# For plotting
import matplotlib as mpl
from matplotlib import pyplot as plt
def ssh():
hamiltonian = "m*sigma_x + alpha * k_x * sigma_y"
def plot(ax, a=1):
params = dict(m=.5, alpha=.5)
h_k = kwant.continuum.lambdify(hamiltonian, locals=params)
k_cont = np.linspace(-1, 1, 201)
e_cont = [scipy.linalg.eigvalsh(h_k(k_x=ki)) for ki in k_cont]
template = kwant.continuum.discretize(hamiltonian, grid=a)
syst = kwant.wraparound.wraparound(template).finalized()
def h_k(k_x):
p = dict(k_x=k_x, **params)
return syst.hamiltonian_submatrix(params=p)
ax.plot(k_cont, e_cont, 'r-')
ax.plot([], [], 'r-', label='continuum')
ax.set_xlim(-1, 1)
ax.set_ylim(-2, 2)
ax.set_title('a={}'.format(a))
ax.set_xlabel('Momentum k_x')
ax.set_ylabel('energy E')
ax.grid()
ax.legend()
_, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(12, 4))
plot(ax1, a=1)
plot(ax2, a=.25)
plt.show()
def main():
ssh()
if __name__ == '__main__':
main()
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*_Thanks in advance,*
import kwant
import kwant.continuum
import scipy.sparse.linalg
import scipy.linalg
import numpy as np
# For plotting
import matplotlib as mpl
from matplotlib import pyplot as plt
def ssh():
hamiltonian = "m*sigma_x + alpha * k_x * sigma_y"
def plot(ax, a=1):
params = dict(m=.5, alpha=.5)
h_k = kwant.continuum.lambdify(hamiltonian, locals=params)
k_cont = np.linspace(-1, 1, 201)
e_cont = [scipy.linalg.eigvalsh(h_k(k_x=ki)) for ki in k_cont]
template = kwant.continuum.discretize(hamiltonian, grid=a)
syst = kwant.wraparound.wraparound(template).finalized()
def h_k(k_x):
p = dict(k_x=k_x, **params)
return syst.hamiltonian_submatrix(params=p)
ax.plot(k_cont, e_cont, 'r-')
ax.plot([], [], 'r-', label='continuum')
ax.set_xlim(-1, 1)
ax.set_ylim(-2, 2)
ax.set_title('a={}'.format(a))
ax.set_xlabel('Momentum k_x')
ax.set_ylabel('energy E')
ax.grid()
ax.legend()
_, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(12, 4))
plot(ax1, a=1)
plot(ax2, a=.25)
plt.show()
def main():
ssh()
if __name__ == '__main__':
main()
