Kwant-discuss June 2022

kwant-discuss@python.org

5 participants
7 discussions

Defining uniaxial strain in specified region of graphene
by shrushti.tapar07＠gmail.com 20 Jan '23

20 Jan '23

I want to create the graphene strained superlattice-like structure, having uniaxial strain defined at the specified region. Please, someone can suggest to me how to define the strained region and interface between unstrained and strained graphene regions. Thanks in Advance Shrushti

4 6

Re: How the spin is positioned in the Smatrix?
by Diego Bruno 26 Sep '22

26 Sep '22

Can you disponibilize the code?

4 3

Gate-defined Nanowire Quantum Dot
by Jonathan Fields 15 Sep '22

15 Sep '22

Dear Reader, I am new to KWANT and trying to figure out if it is suitable for calculating transport properties of gate-defined quantum dots made out of nanowires, along the lines of the structure used in https://arxiv.org/abs/cond-mat/0609463. Now, I understand that the mailing list is not a place to ask people to do my work for me, and my question is also not for someone to do this. What I am looking for is some insights into if this is possible (and not all that difficult) with the package. At first sight (and going through the tutorials as well as the APS March Meeting material) this does not seem straightforward; what I struggle with is how to define this type of dot in KWANT. Now, one way would of course be to built the entire 3D geometry of the system, but this will be computationally expensive, and probably also rather tricky to do in terms of defining everything, from the hexagonal wire itself to all of the gates and oxide layers and such. Some abstraction would be preferred, perhaps even reducing the dimensionality and making a 2D system, such as often done in the tutorial. Is this a good idea? My problem is that if one does this, then I run into the problem of how to model the 'half wrap-around' type gates typically used in these devices. In the transport through barrier section of the APS March Meeting material there is a section on how to model realistic potentials, but this would not work all that well for these wrap around type gates. On the other hand, in a way they are perhaps not so different from the QPC in that section. One could model the three gates as something like https://i.imgur.com/WZC983c.png as they do essentially form channels in the wire. Apart from if this sacrifices too much of the nanowire nature in favor of a 2DEG system, I do suppose such a system should in principle be able to be treated as a quantum dot. I haven't been able to confirm this as I am not yet sure how one can apply a source-drain voltage in KWANT; I first thought that this would probably be related to the energy of the modes, but then again I have not been able to produce Coulomb diamonds in this way. The question is getting rather lenghty, and also a bit unclear at this point. Perhaps I should finish up by stating it in a concise form; would you think that it is possible to simulate the transport of such a gate defined nanowire quantum dot device with KWANT, and if so, is the approach I am suggesting above a viable one, or would you go about it very differently? Kind regards Jonathan <http://aka.ms/weboutlook>

4 4

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