Kwant-discuss June 2022

kwant-discuss@python.org

5 participants
4 discussions

Dispersion Plot of SSH Model with Linearly Varying Chemical Potential
by Subhadeep Chakraborty 27 Jun '22

27 Jun '22

Hi Kwant Users ! I was trying to plot the band structure of the ssh model with linearly varying chemical potential (\mu*x). But it is showing error that "*Expecting an arraylike object or a scalar*" while adding this potential term. Can anyone please tell where I am making mistake and how to rectify it ? _____________________________________ Code is attached below :- import kwant import numpy as np import math ## import matplotlib #matplotlib.use('Agg') ## # For plotting from matplotlib import pyplot as plt # For matrix support import tinyarray I2 = tinyarray.array([[1,0], [0,1]]) Sx = tinyarray.array([[0,1], [1,0]]) Sy = tinyarray.array([[0,-1j], [1j,0]]) Sz = tinyarray.array([[1,0], [0,-1]]) Sp = tinyarray.array([[0,2], [0,0]]) Sm = tinyarray.array([[0,0], [2,0]]) def create_system(length=10): t1 = 0.5 ; t2 = 1.0 ; def Onsite(site): (x, ) = site.pos potential = x return x # system building lat = kwant.lattice.square(a=1, norbs=2) syst = kwant.Builder() # central scattering region syst[(lat(x, 0) for x in range(length))] = t1*Sx syst[lat.neighbors()] = (t2*Sx - 1j*t2*Sy)/2 # add leads sym = kwant.TranslationalSymmetry((-1, 0)) lead_left = kwant.Builder(sym) lead_left[lat(0, 0)] = t1*Sx + Onsite*I2 lead_left[lat.neighbors()] = (t2*Sx - 1j*t2*Sy)/2 syst.attach_lead(lead_left) syst.attach_lead(lead_left.reversed()) return syst def main(): # parameters # create system syst = create_system(length=10).finalized() # plot the system and dispersion kwant.plot(syst) kwant.plotter.bands(syst.leads[0], show=False) plt.plot([-np.pi, np.pi], [chemical_potential, chemical_potential], 'k--') plt.show() lead = syst.leads[0] bands = kwant.physics.Bands(lead) momenta = np.linspace(-2*np.pi, 2*np.pi, 401) energies = [bands(k) for k in momenta] plt.plot(momenta, energies,linestyle='--') plt.xlim(-2*np.pi, 2*np.pi) #pyplot.ylim(-5, 5) plt.xlabel("$k$") plt.ylabel("Energy") #pyplot.axhline(y=0.0, color='k', linestyle='-') plt.tight_layout() plt.grid() plt.show() plt.close() if __name__ == '__main__': main() ________________________________________________ Thanks in advance, *_________________________________* *Subhadeep Chakraborty* *_________________________________*

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Plot Band-Structure of SSH Model with Linearly Varying Chemical Potential Using Kwant.continuum
by Subhadeep Chakraborty 27 Jun '22

27 Jun '22

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. _______________________________________ 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() _______________________________________________________ *_Thanks in advance,*

3 2

Removing a certain hopping in the Kwant.plot
by Sayandip Dhara 03 Jun '22

03 Jun '22

Hello, As I understand that when I use "kwant.plot" to generate a lattice it automatically connects with a line whenever it sees a hopping between two sites. Now in my case, I wanted to connect two edges of a system by hopping to implement periodic boundary conditions. However, now when I plot the lattice I can see the long black lines from one edge to another since they are connected by a hopping. So, when I do a ldos I can still see those lines in my plot. So is there a way to remove the lines corresponding to the hopping between two edges in the plot?

3 3

Removing a certain hopping in the Kwant.plot
by Sayandip Dhara 03 Jun '22

03 Jun '22

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Kwant-discuss June 2022