Mailman 3 October 2020 - Kwant-discuss

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

current-voltage diagram
by loojoo026＠gmail.com 08 Apr '22

08 Apr '22

dear all I have done my project using Kwant and I have drawn a conductance-energy diagram for the system. The question I have is how can I get the current-voltage diagram? thanks Leo

4 4

How the spin is positioned in the Smatrix?
by Qingtian Zhang 06 Mar '22

06 Mar '22

Dear all, I am trying square lattice with spin-orbit coupling and Zeeman splititng just like the example of Tutorial 2.3.1. Now I want to get the spin-dependent conductance：Guu,Gud,Gdu,and Gdd, where "u" indicates up spin, d indicates down spin. We can have the scattering matrix through Smatrix=kwant.smatrix(sys, energy), but how the spin is positioned in the scattering matrix? I have checked some simple cases, it seems the Smatrix is organized like this: | r t | S= | t' r' | but how the spin is included? Thanks in advance. Qingtiian Zhang The code is: import kwant from matplotlib import pyplot from numpy import matrix import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) sys=kwant.Builder() lat=kwant.lattice.square() a=1 t=1.0 alpha=0.5 e_z=0.08 W=2 L=2 sys[(lat(x, y) for x in range(L) for y in range(W))] = \ 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \ -t * sigma_0 - 1j * alpha * sigma_y # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \ -t * sigma_0 + 1j * alpha * sigma_x #### Attach the leads and return the finalized system. #### sys.attach_lead(lead) sys.attach_lead(lead.reversed()) kwant.plot(sys) sys=sys.finalized() print "Hamiltonian=" print sys.hamiltonian_submatrix() Smatrix=kwant.smatrix(sys, energy=3.) print "The scattering matrix=" print matrix.round((Smatrix.data),2) print "T=",(Smatrix.transmission(1, 0))

3 3

Spin polarized transport calculation
by L.M J 06 Mar '22

06 Mar '22

Dear Kwant users and developers I have two questions related to the spin calculation using kwant. 1. I'm wondering if we can do spin-polarized transport in kwant? For example, can we can get the separate Conductance Vs Energy diagram for spin up and spin down terms. I'm thinking one way of doing this is to set up the Rashba Hamiltonian as a whole. And then manually extract the spin up and spin down hamiltonian and do the transport calculation separately. But this will eliminate some extra terms that I don't know whether this is correct anymore. Any suggestions? 2. How can we set up the spin polarization for a particular site? For example, in some of the topological insulator, can we set up spin polarization on the edge as up and the other side of the edge as down, and then do the transport? Or this question is completely wrong? Thanks for advance. Sincerely, Liming

3 3

How to caculate hall resistance
by ZHANG Bing 12 Sep '21

12 Sep '21

Dear Sir, I am a PhD student of Hong Kong University of Science and Technology. I want to use KWANT to caculate Hall resistance of a Hall bar structure.We can get the conductance between 6 electrodes, but how to get hall resistance? Can you give me some help? Thank you very much. Best Regards, Zhang Bing

4 3

To to separate spins, electron and hole
by Khani Hosein 22 Jun '21

22 Jun '21

Dear all, I am using Kwant to study a system with both spins and electron and hole, so the hopping matrix is 4X4. Now I want to know how to separate the spins, electron and hole. I study this through the "2.6. Superconductors: orbital degrees of freedom, conservation laws and symmetries" smatrix = kwant.smatrix(syst, energy) data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -smatrix.transmission((0, 0), (0, 0)) +smatrix.transmission((0, 1), (0, 0))) I do not find more information about this for kwant. For my system, if I have 3 leads, and the hopping and onsite energy is set in this order: (e↑,0,0,0)- spin up electron,first row of the 4X4matrix (0,e↓,0,0)- spin down electron,second row of the 4X4matrix (0,0, h↑ ,0)- spin up hole,third row of the 4X4matrix (0,0, 0, h ↓ )- spin down hole,fourth row of the 4X4matrix I want to obtain the transmissions from 0 →2. smatrix = kwant.smatrix(syst, energy) The transmission from h↑ to e↑ is: smatrix.transmission((2, 1), (0, 2)) The transmission from h ↓ to e↑ is: smatrix.transmission((2, 1), (0, 3)) Is my understanding correct? Thanks very much in advance! Hosein Khani

3 4

how to plot the Charge density with multiple orbitals per site
by Xiangru Kong 13 Nov '20

13 Nov '20

Hi all, I want to plot the the Charge density using kwant.plot method, I want to know how to plot the Charge density in a system with multiple orbitals per site. Here is some pesuo codes: ..... syst = kwant.Builder() ..... model= kwant.wraparound.wraparound(syst).finalized() ham=model.hamiltonian_submatrix (eigen,evecs) = la.eigh(ham) def site_size(i): return 2 * wf[i] / wf.max() kwant.plot(model, site_size=site_size, site_color=(0, 0, 1, 0.3),fig_size=(10,10)); ********* In my codes, I just found len(model.sites)=6, that is the number of sites in the unit cell, however, due to there are multiple orbitals per site, the len(evecs[:,i])=22 orbitals. So I want to know the real infortion when using kwant.plot? Like what I just posted, it only plot evecs[:6,i]**2 functions? Thanks Xiangru

2 4

questions for wraparound in Kwant
by dae han Park 10 Nov '20

10 Nov '20

Dear all I want to draw a contour plot of the first Brillouin zone and band structure along the path of high symmetry points by using Kwant. In Kwant, I know that "kwant.wraparound.plot_2d_bands" function shows the Brillouin zone in 3D. I read a kwant official documentary to find the information that I want, but I couldn't find the solution. My questions are as follows; 1) are there functions in kwant to draw 2D contour plot of the Brillouin zone and the band structure along the path of high symmetry points? 2) If it is not, could I extract data shown from kwant.wraparound.plot_2d_bands? Thank you for reading my email. Sincerely, Daehan Park. ===================================== Department of Physics, Soongsil University, 369, Sangdo-ro, Dongjak-gu, Seoul 156-743, Republic of Korea (South Korea) mail: m31phy(a)gmail.com ===================================== ᐧ

2 1

Wavefuncton at the impurity of a 2D system
by gubbalau＠iisc.ac.in 13 Oct '20

13 Oct '20

Dear Kwant community, I am relatively new to Kwant. I want to see how a single impurity would affect the 2-terminal conductance spectra for various ribbons (with different terminations) of monolayer WTe2. The template for this lattice is taken from [1], which is authored by the creators of Kwant. I replaced the on-site energies for a few of the sites in the scattering region with a large number. Using the codes (from the repository of codes used for [1]) to calculate the conductance, I was able to produce conductance spectra plots of systems with single impurities for different energies. Now, I wanted to look at the wavefunctions at the sites replaced with impurities for both regular ribbon and ribbon with an added impurity site to see how added impurity is causing a change in the conductance spectrum. I know we cannot use the solver "smatrix" as it gives information about propagating modes only in the leads connected to the scattering region. The solver "wave_function" can be used to calculate the wavefunction at a given site of the scattering matrix, but I am not sure whether that would give the system's wavefunction that one requires to analyze the conductance. Can anyone suggest a way to look at the wavefunctions at impurity sites corresponding to its conductance spectrum? Thanks, Uday Ram [1] "The influence of lattice termination on the edge states of the quantum spin Hall insulator monolayer 1T'-WTe2", 10.1103/PhysRevMaterials.3.054206(2018)

1 0

Implementing the BHZ model
by Victor Regis 12 Oct '20

12 Oct '20

Hello all, I'm trying to implement the BHZ model already in the tight-biding model according to the paper [Phys. Rev. B 96, 155302 (2017) or arXiv:1707.03624]. I use the equations (5),(6) and (7), however with no magnetic field. I'm using Kwant's documentation example 2.10 as a guideline (For what I have to do next it's more convenient that I don't use the discretize method). After some struggling I got the band structure of both mine and Kwant's example to be the same, however my spin density is reversed, it's up where it's supposed to be down. So far I haven't figured out why. Also, the main difference between the implementation is only the make_syst part, all the plotting in my code are snippets from Kwant's discretize.py; My code is below: import kwant import matplotlib.pyplot as plt import numpy as np import random as rd from math import * import matplotlib as mpl import tinyarray sigma_0 = tinyarray.array([[1, 0], [0, 1]]) sigma_x = tinyarray.array([[0, 1], [1, 0]]) sigma_y = tinyarray.array([[0, -1j], [1j, 0]]) sigma_z = tinyarray.array([[1, 0], [0, -1]]) Id = np.eye(4) G1 = np.kron(sigma_z,sigma_x) G2 = -np.kron(sigma_0,sigma_y) G5 = np.kron(sigma_0,sigma_z) def make_syst(a=20,A=3.65, B=-68.6, D=-51.1, M=-0.01, C=0,L=200,W=200): lat = kwant.lattice.square(a,norbs=4) syst = kwant.Builder() def square(pos): (x, y) = pos return (0 <= y < W and 0 <= x < L) def onsite(site): (x, y) = site.pos return C*Id+M*G5-(4/a**2)*(D*Id+B*G5) #equation 5 def hoppingx(site1,site2): return (1/a**2)*(D*Id+B*G5)+(1j/(2*a))*(A*G1) #eq 6 def hoppingy(site1,site2): return (1/a**2)*(D*Id+B*G5)-(1j/(2*a))*(A*G2) #eq 7 syst[lat.shape(square,(0,0))] = onsite syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = hoppingx syst[kwant.builder.HoppingKind((0,1), lat, lat)] = hoppingy def lead_shape(pos): (x, y) = pos return (0 <= y < W) #### Define the left lead. #### lead = kwant.Builder(kwant.TranslationalSymmetry((-a, 0))) lead[lat.shape(lead_shape,(0,0))] = onsite # hoppings in x-direction lead[kwant.builder.HoppingKind((1, 0), lat, lat)] =hoppingx # hoppings in y-directions lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = hoppingy return syst,[lead,lead.reversed()] def main(): syst,leads = make_syst(W=1000,L=2000) # Attach the leads to the system. for lead in leads: syst.attach_lead(lead) # Finalize the system. syst = syst.finalized() # Check that the system looks as intended. #kwant.plot(syst) # Compute the band structure of lead 0. kwant.plotter.bands(syst.leads[0], momenta=np.linspace(-0.3, 0.3, 201), show=False) plt.grid() plt.xlim(-.3, 0.3) plt.ylim(-0.05, 0.05) plt.xlabel('momentum [1/A]') plt.ylabel('energy [eV]') plt.show() wf = kwant.wave_function(syst, energy=0) # prepare density operators sigma_z = np.array([[1, 0], [0, -1]]) prob_density = kwant.operator.Density(syst, np.eye(4)) spin_density = kwant.operator.Density(syst, np.kron(sigma_z, np.eye(2))) # calculate expectation values and plot them wf_sqr = sum(prob_density(psi) for psi in wf(0)) # states from left lead rho_sz = sum(spin_density(psi) for psi in wf(0)) # states from left lead fig, (ax1, ax2) = plt.subplots(1, 2, sharey=True, figsize=(16, 4)) kwant.plotter.map(syst, wf_sqr, ax=ax1) kwant.plotter.map(syst, rho_sz, ax=ax2) ax = ax1 im = [obj for obj in ax.get_children() if isinstance(obj, mpl.image.AxesImage)][0] fig.colorbar(im, ax=ax) ax = ax2 im = [obj for obj in ax.get_children() if isinstance(obj, mpl.image.AxesImage)][0] fig.colorbar(im, ax=ax) ax1.set_title('Probability density') ax2.set_title('Spin density') plt.show() # Call the main function if the script gets executed (as opposed to imported). # See <http://docs.python.org/library/__main__.html>. if __name__ == '__main__': main() Regards, Victor Regis

1 0

Kwant-discuss October 2020