Mailman 3 March 2024 - Kwant-discuss

[kwant] How to make a finite lead?
by 김봉수 12 Jun '24

12 Jun '24

Dear kwant users, I am trying to reproduce the paper following. https://arxiv.org/abs/1110.4280 (in this paper, fig5, 6 will help to understand my questions.) What I’m struggling with now is to build a finite(not infinite, and not having any translational symmetry) lead as below. I wonder 1. I think "kwant.builder.SelfEnergyLead()” function might be proper thing to build a finite lead without any translational symmetry. Is it correct? 2. If it's right, when I run this code using SelfEnergyLead(), the following error occurs. How can I solve it? ------------------------------------------------------------------------------------------------ lat = kwant.lattice.chain(norbs=1) syst = kwant.Builder() syst[(lat(i) for i in range(4))] = 4 syst[lat.neighbors()] = -1 def self_energy(energy, args=(), *, params=None): return -1j left_lead = kwant.builder.SelfEnergyLead(self_energy, interface=[lat(0)], parameters = []) right_lead = kwant.builder.SelfEnergyLead(self_energy, interface=[lat(3)], parameters = []) syst.leads.append(left_lead) syst.leads.append(right_lead) syst = syst.finalized() H = syst.leads[0].kwant.hamiltonian_submatrix kwant.plot(syst) ------------------------------------------------------------------------------------------------ AttributeError: 'SelfEnergyLead' object has no attribute ‘kwant' Any help is appreciated! Best, Bongsu Kim

2 2

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

1 1

Looking for a Tutorial on Quantum Hall Effect Computation Learning
by araya0sun＠gmail.com 20 Mar '24

20 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

4 8

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…

2 1

Distinguisch Scattering matrix Elements
by Lorenzo BAGNASACCO 08 Mar '24

08 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!

2 1

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)

1 0