Mailman 3 February 2020 - Kwant-discuss

To to separate spins, electron and hole
by Khani Hosein Oct. 11, 2024

Oct. 11, 2024

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

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Realistic values of hopping parameters
by Yu Li Oct. 19, 2023

Oct. 19, 2023

Dear all, Now I’m studying some transport property based on multilayered system, with nonmagnetic layer/ferromagnetic layer (NM/FM) stack. May I ask when creating a tight binding system, and setting hoppings by the following function: syst[(lat(1, 0), lat(1, 1))] = t, how to associate the hopping with a realistic system? Such as hoppings between FM and FM atoms, or between FM and NM atoms? I found in many literatures people just simply put t=1, but I assume the value should depend on the type of atoms. My another question is, is it possible to define more than one type of hopping between two sites? For the tight-binding approximation of p electrons, there are two types of hopping integrals: Vppσ, and Vppπ, so I’m wondering if it’s possible to simulate the effect of both hoppings? Thanks a lot for reading my questions! Cheers, Yu Li

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Gate-defined Nanowire Quantum Dot
by Jonathan Fields Sept. 15, 2022

Sept. 15, 2022

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>

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How the spin is positioned in the Smatrix?
by Qingtian Zhang March 6, 2022

March 6, 2022

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))

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Spin polarized transport calculation
by L.M J March 6, 2022

March 6, 2022

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

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How to caculate hall resistance
by ZHANG Bing Sept. 12, 2021

Sept. 12, 2021

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

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different lattices for the scattering region
by tavakkolidjawad March 13, 2020

March 13, 2020

Hello everyone I want to use different lattices structure (honeycomb and diamond) for the scattering region. if I have a honeycomb structure, is it possible in Kwant to add sites from the diamond structure to the system and add hoppings from these sites to the sites from the honeycomb lattice? I have already read Section 2.11 (https://kwant-project.org/doc/1/tutorial/faq#how-to-use-different-lattices-…) in the documentation but this is challenging for me and I have no idea how to solve it. Thanks

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Plotting edge states
by Luca Lepori Feb. 26, 2020

Feb. 26, 2020

Dear Kwant developers and users, I write concerning a doubt that I encountered trying to study by Kwant a model for the quantum Hall/quantum spin Hall effect. In particular, I am focusing on the two-dimensionakl BHZ model, first proposed in the famous paper https://science.sciencemag.org/content/314/5806/1757 Notice that first I keep only one of the two time-reversal-connected blocks forming the quantum spin Hall system (when the mass parameter M is positive); it is known that each block describes a quantum Hall system (again for M >0, otherwise a trivial insulator occurs). I attach below my defining code (included in the % lines) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% import kwant from kwant.digest import uniform # a (deterministic) pseudorandom number generator import math from matplotlib import pyplot as plt import cmath import scipy.sparse.linalg as sla import scipy.linalg as la import numpy from numpy import linalg as LA # For plotting from matplotlib import pyplot # For matrix support import tinyarray #import progressbar #----------------------------------------------------- # We define the variables and the constants a = 1 #lattice step #t = 1 #along x and y #----------------------------------------------------- nullmatrix = tinyarray.array([[0, 0], [0, 0]]) matid = tinyarray.array([[1, 0], [0, 1]]) sigma_0 = tinyarray.array([[1, 0], [0, -1]]) sigma_xp = tinyarray.array([[1, -1j], [-1j, -1]]) sigma_yp = tinyarray.array([[1, 1/2], [-1/2, -1]]) ----------------------------------------------------------------------------------------------------------------- def sistema_BHZ_2e(Lx, Ly, M) : syst = kwant.Builder() lat = kwant.lattice.square(norbs=2) for i in range(0,Lx): #syst[lat(i, 0), lat(i, L - 1)] = sigma_yp for j in range(0,Ly): # On-site Hamiltonian syst[lat(i, j)] = (M - 4)*sigma_0 # Hopping in y-direction if i > 0: syst[lat(i, j), lat(i - 1, j)] = sigma_xp # Hopping in z-direction if j > 0: syst[lat(i, j), lat(i, j - 1)] = sigma_yp return syst %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Correspondingly to what described above, I would expect to see, when M >0, edge modes. Indeed, I obtain them calculating the local densities via the KPM (approximate) method working in Kwant: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% # Plot several local density of states maps in different subplots def plot_ldos(syst, densities, file_name=None): step = 0.1 fig, axes = plt.subplots(1, len(densities), figsize=(7*len(densities), 7)) for ax, (title, rho) in zip(axes, densities): kwant.plotter.density(syst,rho.real, colorbar=True, ax=ax, relwidth = step) ax.set_title(title) ax.set(adjustable='box', aspect='equal') plt.show() plt.clf() -------------------------------------------------------------------------------------------------------------- M = 2 L = 16 Lx = L Ly = L syst = sistema_BHZ_2e(Lx, Ly, M) syst = syst.finalized() hamat = syst.hamiltonian_submatrix(sparse = False) evals, evecs = la.eigh(hamat) kwant_op = kwant.operator.Density(syst, sum=False) local_dos = kwant.kpm.SpectralDensity(syst, operator=kwant_op) print("first negative energy =", evals[int(Lx*Ly-1)]) print("first_positive_energy =", evals[int(Lx*Ly)]) first_negative_energy_ldos = local_dos(energy=evals[int(Lx*Ly-1)]) first_positive_energy_ldos = local_dos(energy=evals[int(Lx*Ly)]) plot_ldos(syst, [('first negative energy', first_negative_energy_ldos),('first positive energy', first_positive_energy_ldos)]) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% I attach below a typical output (KPM.pdf). However, when I calculate the same densities not using the KPM approach (then via the exact function kwant.operator.Density(syst) only ) , that means by the code: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% M = 2 L = 16 Lx = L Ly = L syst = sistema_BHZ_2e(Lx, Ly, M) syst = syst.finalized() hamat = syst.hamiltonian_submatrix(sparse = False) evals, evecs = la.eigh(hamat) kwant_op = kwant.operator.Density(syst, sum=False) print("first negative energy =", evals[int(Lx*Ly-1)]) print("first_positive_energy =", evals[int(Lx*Ly)]) first_negative_energy_ldos = kwant_op(evecs[int(Lx*Ly-1)]) first_positive_energy_ldos = kwant_op(evecs[int(Lx*Ly)]) plot_ldos(syst, [('first negative energy', first_negative_energy_ldos),('first positive energy', first_positive_energy_ldos)]) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% I obtain a totally different density profile, not displaying edge localization (see No_KPM.pdf attached below). I do not understand the reason of such a mismatch. Can you help me ? Thank you very much and best, L.

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Discretizing continuous Hamiltonians
by Khani Hosein Feb. 21, 2020

Feb. 21, 2020

Dear all, I want to discrete the continuous Hamiltonians in PRL 111, 156402 (2013) and calculate the band structure of the ribbon. So I change the parameters of the code in "Tutorial 2.10. Discretizing continuous Hamiltonians". But I can not obtain the same band structure as shown in Fig.3(b) of the PRL paper. Could you please help me to check my attached code? Thanks! Yours sincerely Hosein Khani ########################### 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 qsh_system(a=20, L=4000, W=5000): hamiltonian = """ + C * identity(4) + M * kron(sigma_0, sigma_z) - B * (k_x**2 + k_y**2) * kron(sigma_0, sigma_z) - D * (k_x**2 + k_y**2) * kron(sigma_0, sigma_0) + A * k_x * kron(sigma_z, sigma_x) - A * k_y * kron(sigma_0, sigma_y) """ template = kwant.continuum.discretize(hamiltonian, grid=a) def shape(site): (x, y) = site.pos return (0 <= y < W and 0 <= x < L) def lead_shape(site): (x, y) = site.pos return (0 <= y < W) syst = kwant.Builder() syst.fill(template, shape, (0, 0)) lead = kwant.Builder(kwant.TranslationalSymmetry([-a, 0])) lead.fill(template, lead_shape, (0, 0)) syst.attach_lead(lead) syst.attach_lead(lead.reversed()) syst = syst.finalized() return syst def analyze_qsh(): #######the follwing parameters are given to make sure the hamiltonian is the same as ####### PRL 111, 156402 (2013) AP=0.02851 BP=(0.4381-0.2081)/2. DP=(0.4381+0.2081)/2. MP=(-0.19808+0.19153)/2. CP=(-0.19808-0.19153)/2. params = dict(A=AP, B=BP, D=DP, M=MP, C=CP) syst = qsh_system() kwant.plotter.bands(syst.leads[0], params=params, momenta=np.linspace(-0.3, 0.3, 201), show=False) plt.grid() plt.xlim(-.3, 0.3) plt.ylim(-0.2, -0.19) plt.xlabel('momentum [1/A]') plt.ylabel('energy [eV]') plt.show() # get scattering wave functions at E=0 wf = kwant.wave_function(syst, energy=0, params=params) # 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 kwant.plotter.map(syst, wf_sqr, show=False) plt.show() def main(): analyze_qsh() # 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()

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Idea discussion: development internships
by Anton Akhmerov Feb. 14, 2020

Feb. 14, 2020

Hi everyone! Together with the other Kwant authors I am planning a grant application. One activity for which we consider requesting support is a series of internships—visits to one of our groups with the goal of developing either a Kwant feature or a related project. These internships would last for perhaps a couple of months, with the idea that by the end of the visit, they result in something either implemented or being close to completion. We think that this work organization would benefit everyone involved, and we'm very much interested to explore this idea. Still, before we commit to that, we would be very much interested to hear everyone's opinion: Would you or someone you know want to go for such an internship? What do you think of this idea overall? Any idea of what project could be useful? Cheers, Anton

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