Mailman 3 - Kwant-discuss

Kwant-compatible Hartree-Fock Package
by Johanna 03 Jun '24

03 Jun '24

Hi all, We're excited to share a new Python package we've developed at the Quantum Tinkerer group: MeanFi. MeanFi is a self-consistent Hartree-Fock solver for tight-binding models designed to work smoothly with Kwant. Our algorithm is optimized to easily and extensibly perform all your mean-field calculations. We made it such that you can: 1) define the initial Hamiltonian and the density-density interaction as Kwant models, 2) turn it into a tight-binding format, 3) find the groundstate solution, and 4) finally turn it back to a Kwant system to do all the analysis you want! You can find the documentation, tutorials, and installation instructions here: <https://meanfi.readthedocs.io/en/latest/>. We welcome your feedback and contributions. If you have any questions or run into issues, feel free to reach out or open an issue on GitHub here: <https://github.com/quantum-tinkerer/MeanFi>. All the best, MeanFi Developers Kostas, Johanna, Anton and Antonio

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Questions About Magnetic Field Units in Landau_level.py for Landau Level Calculations
by ac76888＠sjtu.edu.cn 30 May '24

30 May '24

Dear Kwant Community, I am writing to seek assistance with two issues I have encountered while using Kwant for solving transport problems. Your guidance would be greatly appreciated. 1. I am trying to calculate the Landau levels of monolayer graphene using the following Hamiltonian (python): ``` hamiltonian = """ + hbar_vF * (k_x * kron(sigma_0, sigma_x) + k_y * kron(sigma_0, sigma_y)) """ params = dict(hbar_vF=6.582) ``` In the documentation for the `discretize_landau` function, it is stated that "The units of magnetic field are :math:`ϕ₀ / 2 π a²` with :math:`ϕ₀ = h/e` the magnetic flux quantum and :math:`a` the unit length." Is a^2 here the area (A) of a primitive cell of graphene (A = 5.24 Å²)? How can I convert this unit into Tesla? 2. Can I use this code to calculate the Landau levels of multilayer stacking graphene with a sequences of hoppings ? Are there specific considerations or modifications I should be aware of when extending the calculation to multilayer graphene? Thank you in advance for your help. Best regards, ac76888

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Current density for given lead currents
by X.-X. Zhang 15 May '24

15 May '24

Hello Kwant community, I am considering a 6-terminal sample with 0,1,2,3 the voltage leads and 4,5 the current lead. Normally, with the conductance_matrix M found by kwant I can calculate transport properties (the voltages in vector V) as per the linear equation I = M V, given I = [0,0,0,0,1,-1]. Now I want to plot the current density corresponding to this transport state, but not sure how to do it. For instance, with wf = kwant.wave_function(sys, energy), I can have all scattering wavefunctions wf(4) incoming from the current lead 4. But how to (or is it necessary to) reflect the above current configuration vector I we specified? I presume the current density may vary with different I vectors. Or maybe I misunderstand some basics? Thank you!

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wave function amplitude square meaning in kwant setting
by YIGITHAN GEDIZ 14 May '24

14 May '24

Hi all, I have a scattering region, where for a given energy E, there is a single propagating mode. (kwant.wave_function(sys, E).shape[0] == 1) When I increase the energy a little bit without leaving the same band and plot the wavefunction again, I observe the same pattern in the scattering region, but the amplitudes are different. First one's maximum amplitude square is 6, whereas the other one's is 4, for instance. I observe that this is somehow related to the density of states at given energies, such that higher maximum amplitude corresponds to higher DOS, but I did not understand why. What does wave function's amplitude square mean in kwant? I tried to investigate the source code but I failed. Thank you very much for your time

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About the Warning "Hamiltonian breaks Conservation law, ignoring the symmetry in the computation.."
by GUIDO MENICHETTI 04 May '24

04 May '24

Dear developers, dear all, I am Guido Menichetti, a Post-Doc at the University of Pisa. I am currently working on computing the Andreev reflection in a 3D hexagonal lattice system, incorporating the spin degree of freedom and utilizing wraparound techniques. To facilitate this, I have been following the Kwant tutorial available at https://kwant-project.org/doc/1.0/tutorial/tutorial5. In my approach, I define a "conservation law" to decompose the transmission function into four blocks: two for the spin degree of freedom and two for the electron-hole degree of freedom. Initially, I successfully ran calculations in a 2D system with periodic boundary conditions, perpendicular to the transport direction, without encountering any warning messages. However, when attempting the same calculations in a 3D system with periodic boundary conditions in the perpendicular directions, I encountered a warning message: "[...] |envs\Kwant-env\lib\site-packages\kwant\system.py:316: UserWarning: Hamiltonian breaks Conservation law, ignoring the symmetry in the computation warnings.warn('Hamiltonian breaks ' + name +". This warning disappears when I set the superconductor gap Delta (as defined in https://kwant-project.org/doc/1.0/tutorial/tutorial5) to 0 (Delta = 0). The superconducting part is located in the right lead. I believe the issue does not stem from the Hamiltonian of the scattering region. However, I am puzzled by the origin of this warning and its potential impact on the results. Could this problem be related to the "wraparound" technique in the 3D system? The only difference between the 2D and 3D systems is the lattice: the 2D system lives on a square lattice, while the full 3D system is a hexagonal lattice. Your insights and guidance on resolving this issue would be greatly appreciated. Best regards, Guido Menichetti University of Pisa

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The method of using ‘’kwant.lattice.general‘’
by araya0sun＠gmail.com 22 Mar '24

22 Mar '24

Dear kwant users, Hello everyone, while using Kwant, I noticed that in the tutorials, a square lattice (a=1) is used for building structures. However, in the graphene tutorial, 'kwant.lattice.general' is used, with the following code: -------------- graphene = kwant.lattice.general([[1, 0], [1/2, np.sqrt(3)/2]], # lattice vectors [[0, 0], [0, 1/np.sqrt(3)]]) # Coordinates of the sites a, b = graphene.sublattices --------------- Attached is the image of the graphene lattice. I have found the method for using kwant.lattice.general: kwant.lattice.general(prim_vecs, basis=None, name='', norbs=None) But when it comes to the mentioned graphene, I cannot understand the usage of '’kwant.lattice.general’' The code mentions that the lattice vectors are ‘'[1, 0], [1/2, np.sqrt(3)/2]’', which appears to be a parallelogram. I assume it corresponds to a unit cell. However, the code mentions '’[[0, 0], [0, 1/np.sqrt(3)]]'’ as ‘'Coordinates of the sites'’, and I don't understand which two atoms it corresponds to. Can any scholar help me resolve my doubts? My second question is, when using Kwant, do I need to input the lattice constant? If so, where should it be written? Best wishes. Sincerely, Araya

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Looking for a Tutorial on Quantum Hall Effect Computation Learning
by araya0sun＠gmail.com 21 Mar '24

21 Mar '24

Dear all Kwant users， Hi,I have tried using Kwant to draw and build systems, and now I want to learn about computing the Hall effect. However, I couldn't find relevant information in the Kwant 1.4.3 documentation. Nevertheless, I saw some users mentioning Hall effect computations on the community, such as the program 'qhe.py'. But I couldn't find related code or tutorials. Could any knowledgeable users help me with this? I would greatly appreciate it.Thank you very much and best wishes. Sincerely, Araya

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fill command continuum Hamiltonian
by jorge huamani 19 Mar '24

19 Mar '24

Dears, Is it possible to obtain a finite system with three different regions using a discretize continuum Hamiltonian approach? I am using the fill command but I have issues obtaining a finite system, my idea is to have a finite system and fill each part of the system with different Hamiltonian talking about those three regions. I would appreciate if you have any idea to make it, thank in advance Best regards, -- Dr. Jorge Huamaní Correa Professor at Universidad Tecnológica del Perú CTI Vitae : https://ctivitae.concytec.gob.pe/appDirectorioCTI/VerDatosInvestigador.do?i…

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Distinguisch Scattering matrix Elements
by Lorenzo BAGNASACCO 09 Mar '24

09 Mar '24

Hi everyone! I am a beginner Kwant consumer and, for this reason, I am trying to "solve" very simple problems, i.e. problems for beginners. The first one is the following: I have a 1D problem where basically a spin-1/2 particle crosses a region without a potential neither magnetic fields. I am able to write correctly the setup of the problem in Kwant. Fixed the incoming particle energy, I find a 4 by 4 scattering matrix (this is comforting), but I do not understand which is the protocol that Kwant uses to order the coefficients in the scattering matrix. For example, according to the usual description of the transmission matrix (from left-to-right), the element t_{00} corresponding to the probability to start, for example, in the state s=-1/2 in the left lead and arrives in the state s=-1/2 in the right lead, and similarly for the other elements. How can I manage these labeling in my code? Thank you!

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Problem about Landau level
by 李家丞 C24096041 06 Mar '24

06 Mar '24

Dear everyone: we know that enegy gap in Landau levels is hw, then we can know the magnitude of magnatic field by claculating the gap between landau levels, in this code, the magnitude of magnetic field I set is way different by calculating the energy gap in Landau levels in this code, Ihave no idea what went wrong, so I'll be thankful if you can konw what is wrong in this code. Thank you Following is my code—-————————————————- ### Import modules ### import kwant import numpy as np from math import pi from matplotlib import pyplot as plt import csv import scipy.sparse.linalg as sla a = 1 # Lattice constant, in nm h = 4.14e-15 # Plank's constnt in unit of eV*s hbar = 6.58e-16 # In unit of eV*s m = 9.11e-31 # Mass of electron in kg q = 1.6e-19 # Charge of an electron in coulomb t = hbar*hbar/(2*m*a*a) # t = hbar^2/(2m(a^2)) B = 3 # Magnitude of external magnetic field, in unit of Tesla phi0 = 4.14e-15 # Magnetic quantum def setup_system(W=100, L=100): ### Define a function about hopping ### def hopping(hop): x1, y1 = hop[0].pos # Get the position imformation of site_1 x2, y2 = hop[1].pos # Get the position imformation of site_2 delta_x = (x2 - x1) * 1e-9 # Differance of x coordinate in nanometer y_bar = (y1 + y2) / 2 * 1e-9 # Averge of y coordinate in nanometer return delta_x, y_bar ### Define the shape of the system ### def rectangle(pos): x, y = pos return x > -W and x < W and y > -L and y < L ### Define the shape of the lead ### def lead_shape(pos): x, y = pos return (-L < y < L) ### Set up the system ### sys = kwant.Builder() # Builde up the system lat = kwant.lattice.square(a, norbs = 1) # Set up the lattice in shape of square sys[lat.shape(rectangle, (0, 0))] = 4 * t # Define the on-site energy for hopx in kwant.builder.HoppingKind((1, 0), lat)(sys): # Define the hopping in x-direction delta_x, y_bar = hopping(hopx) phase = 2* pi /phi0 *B *delta_x *y_bar # Phase differnce due to magnetic field sys[hopx] = -t * np.exp( phase*1j) for hopy in kwant.builder.HoppingKind((0, 1), lat)(sys): # Define the hopping in y-direction sys[hopy] = -t ### Set up the left lead ### lead0 = kwant.Builder(kwant.TranslationalSymmetry((-1, 0))) # The current goes from the left lead lead0[lat.shape(lead_shape, (0, 0))] = 4 * t # Define the on-site energy for hopx in kwant.builder.HoppingKind((1, 0), lat)(lead0): # Define the hopping in x-direction delta_x, y_bar = hopping(hopx) phase = 2* pi /phi0 *B *delta_x *y_bar # Phase differnce due to magnetic field lead0[hopx] = -t * np.exp( phase*1j) for hopy in kwant.builder.HoppingKind((0, 1), lat)(lead0): # Define the hopping in y-direction lead0[hopy] = -t ### Set up the right lead ### lead1 = kwant.Builder(kwant.TranslationalSymmetry((1, 0))) # The current goes from the left lead lead1[lat.shape(lead_shape, (0, 0))] = 4 * t # Define the on-site energy for hopx in kwant.builder.HoppingKind((1, 0), lat)(lead1): # Define the hopping in x-direction delta_x, y_bar = hopping(hopx) phase = 2* pi /phi0 *B *delta_x *y_bar # Phase differnce due to magnetic field lead1[hopx] = -t * np.exp( phase*1j) for hopy in kwant.builder.HoppingKind((0, 1), lat)(lead1): # Define the hopping in y-direction lead1[hopy] = -t ### Attach the left lead and the right lead ### sys.attach_lead(lead0) sys.attach_lead(lead1) ### Finalize the system ### sys = sys.finalized() ### Finally, return the system ### return sys sys = setup_system() ### Compute, plot and store the bandstructure ### def plot_bandstructure(flead, momenta): bands = kwant.physics.Bands(flead) energies = [bands(k)[0: 10] for k in momenta] bandenergy = [] '''np.savetxt("Momentatest_l.csv", momenta, delimiter = ",") for i in range(1000): bandenergy.append(energies[i]) np.savetxt("Band_energytest1_l.csv", bandenergy, delimiter = ",")''' plt.figure(figsize=(6, 8)) plt.plot(momenta, energies, color='k') plt.xlabel("momentum [a^-1]") plt.ylabel("energy [eV]") plt.ylim(0, 0.03) plt.xlim(-1, 1) plt.show() #kwant.plotter.bands(sys.leads[0]) momenta = np.linspace(-1, 1, 1000) plot_bandstructure(sys.leads[0], momenta) plot_bandstructure(sys.leads[1], momenta)

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