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
Hello Kwant users,
I am trying to compare the retarded Green's function of a simple 1D wire
attached to two leads using two different methods:
(I) Using scattering wave function obtained from the Kwant software and
using Eq. 25 in energy domain of "Numerical simulations of time resolved
quantum electronics (https://arxiv.org/abs/1307.6419) written by Kwant
authors.
(II) Direct computation of the retarded Green's function by inverting
device Hamiltonian with self energies of the attached leads (again computed
from the Kwant software): G^r(E) = [E+\i*\eta - H- \Sigma^r_{leads}]^{-1}
for a relatively small system size (5 sites in the attached example). Here
both H and \Sigma^r are computed from the Kwant software.
However, I find that these two results do not agree even in a simple 1D
example when on-site potential is present in the few sites of device or
scattering region only.
I have attached the Python script with this email.
Does anyone know the reason behind the discrepancy between the two
methods?I would greatly appreciate any comments/suggestions on how we can
resolve this error?
Thanks!
Dear Sir,
I am trying to plot the energy as a function of magnetic field for a 3D
case, but I am getting tedious results. The system is infinite in two
directions and has some width in the third direction. Please have a look at
the code attached below. I tried a lot but failed. Is the code correct or I
am wrong somewhere.
Thank you.
*import kwantimport scipy.sparse.linalg as slaimport matplotlib.pyplot as
pltimport tinyarrayimport numpy as npfrom numpy import cos, sin, piimport
cmathfrom cmath import expsigma_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]])def make_system(a=1, L=30, W=10, H=10, t=1.0, t_x=1.0, t_y=1.0,
t_z=1.0, lamda=0.1, beta=1.05): def onsite(site): return (t_z *
cos(beta) + 2 * t) * sigma_z def hoppingx(site0, site1):
return (-0.5 * t * sigma_z - 0.5 * 1j * t_x * sigma_x) def
hoppingy(site0, site1): return -0.5 * t * sigma_z - 0.5 * 1j * t_y *
sigma_y def hoppingz(site0, site1, B): y = site1.pos[1]
return (-0.5 * t_z * sigma_z - 0.5 * 1j * lamda * sigma_0) * exp(2 * pi *
1j * B * a * (y-40)) syst = kwant.Builder() lat =
kwant.lattice.cubic(a) syst[(lat(z, y, x) for z in range(H) for y in
range(W) for x in range(L))] = onsite syst[kwant.builder.HoppingKind((1,
0, 0), lat, lat)] = hoppingz syst[kwant.builder.HoppingKind((0, 1, 0),
lat, lat)] = hoppingy syst[kwant.builder.HoppingKind((0, 0, 1), lat,
lat)] = hoppingx
lead1=kwant.Builder(kwant.TranslationalSymmetry((0,-a,0)))
lead1[(lat(z,y,x) for z in range(H)for y in range(W)for x in
range(L))]=onsite lead1[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
= hoppingz lead1[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
hoppingy lead1[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
hoppingx syst.attach_lead(lead1) syst.attach_lead(lead1.reversed())
lead2=kwant.Builder(kwant.TranslationalSymmetry((-a,0,0)))
lead2[(lat(z,y,x) for z in range(H)for y in range(W)for x in
range(L))]=onsite lead2[kwant.builder.HoppingKind((1, 0, 0), lat, lat)]
= hoppingz lead2[kwant.builder.HoppingKind((0, 1, 0), lat, lat)] =
hoppingy lead2[kwant.builder.HoppingKind((0, 0, 1), lat, lat)] =
hoppingx syst.attach_lead(lead2) syst.attach_lead(lead2.reversed())
syst = syst.finalized() return systdef analyze_system(): syst =
make_system() kwant.plot(syst) Bfields = np.linspace(0, 0.002, 100)
energies = [] for B in Bfields: ham_mat =
syst.hamiltonian_submatrix(params=dict(B=B), sparse=True) ev, evec =
sla.eigsh(ham_mat.tocsc(), k=20, sigma=0) energies.append(ev)
#print(energies) plt.figure() plt.plot(Bfields, energies)
plt.xlabel("magnetic field [${10^-3 h/e}$]") plt.ylabel("energy [t]")
plt.ylim(0, 0.11) plt.showdef main(): syst = make_system()
analyze_system()main()*
--
With Best Regards
NAVEEN YADAV
Ph.D Research Scholar
Deptt. Of Physics & Astrophysics
University Of Delhi.
Dear users,
Good day.
My query is about hoppings.
In fact, sometimes we have to change the onsite parameters when for
instance a magnetic field is applied.
What is the difference between hop[0].tag and hop[1].tag
My second question
the onsite fuction for example: def onsite(site, V):return V
why it depends on site where the shape functions for example
def circle(pos): rsq = pos[0] ** 2 + pos[1] ** 2
depends on pos
Best
A BELAYADI
Dear Sir,
I have a problem to install Kwant when download the Pre-built packages ( Anaconda package ). That is to say I can't download the package. My operating systems is Microsoft Windows. Can you help me.
Best regards,
Chunxu Bai
Hi,
> We consider the values of the conservation law based on the
> off-diagonal term of Hamiltonian matrix, details are as follows:
>
>
>
> H = tinyarray.array([[0, 0, 0, 1, 0, 0],
>
> [0, 0, 0, 0, 1, 0],
>
> [0, 0, 0, 0, 0, 1],
>
> [1, 0, 0, 0, 0, 0],
>
> [0, 1, 0, 0, 0, 0],
>
> [0, 0, 1, 0, 0, 0]])
>
I don't really understand; is this the full Hamiltonian?
> spin_block = tinyarray.array([[0, 0, 0, 1, 0, 0],
>
> [0, 0, 0, 0, 1, 0],
>
> [0, 0, 0, 0, 0, 1],
>
> [-1, 0, 0, 0, 0, 0],
>
> [0, -1, 0, 0, 0, 0],
>
> [0, 0, -1, 0, 0, 0]])
>
> And we add “conservation_law= - spin_block” in “lead=kwant.Builder()”
>
>
>
> The program can not work, and prompt error:
>
>
>
> IndexError: index 2 is out of bounds for axis 0 with size 2
>
There is not enough information for me to be able to help you. Please
attach a complete Kwant script.
Happy Kwanting,
Joe
Dear Yan,
If you post a small part of your program reproducing this error message,
someone may help you.
Regards,
Adel
On Mon, Sep 9, 2019 at 12:58 PM X.F.Yan <yxf0125(a)aliyun.com> wrote:
>
>
> Dear sir,
>
>
> Recently, we use Kwant to solve for Hamiltonian matrix with off-diagonal
> terms. We successfully calculate the energy band structure and total
> conductance. But unfortunately, we tried to compute the spin conductance
> without success.
>
>
>
> We consider the values of the conservation law based on the off-diagonal
> term of Hamiltonian matrix, details are as follows:
>
>
>
> H = tinyarray.array([[0, 0, 0, 1, 0, 0],
>
> [0, 0, 0, 0, 1, 0],
>
> [0, 0, 0, 0, 0, 1],
>
> [1, 0, 0, 0, 0, 0],
>
> [0, 1, 0, 0, 0, 0],
>
> [0, 0, 1, 0, 0, 0]])
>
>
>
>
>
>
>
> spin_block = tinyarray.array([[0, 0, 0, 1, 0, 0],
>
> [0, 0, 0, 0, 1, 0],
>
> [0, 0, 0, 0, 0, 1],
>
> [-1, 0, 0, 0, 0, 0],
>
> [0, -1, 0, 0, 0, 0],
>
> [0, 0, -1, 0, 0, 0]])
>
> And we add “conservation_law= - spin_block” in “lead=kwant.Builder()”
>
>
>
> The program can not work, and prompt error:
>
>
>
> IndexError: index 2 is out of bounds for axis 0 with size 2
>
>
>
> Please help me.
>
>
>
> Thank you,
>
>
>
> Kind regards,
>
> X.F.Yan
>
>
>
>
>
>
>
--
Abbout Adel
Dear sir,
Recently, we use Kwant to solve for Hamiltonian matrix with off-diagonal terms. We successfully calculate the energy band structure and total conductance. But unfortunately, we tried to compute the spin conductance without success.
We consider the values of the conservation law based on the off-diagonal term of Hamiltonian matrix, details are as follows:
H = tinyarray.array([[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1],
[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0]])
spin_block = tinyarray.array([[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1],
[-1, 0, 0, 0, 0, 0],
[0, -1, 0, 0, 0, 0],
[0, 0, -1, 0, 0, 0]])
And we add “conservation_law= - spin_block” in “lead=kwant.Builder()”
The program can not work, and prompt error:
IndexError: index 2 is out of bounds for axis 0 with size 2
Please help me.
Thank you,
Kind regards,
X.F.Yan
I am trying to plot the wavefunction for a 2D NISIN Hamiltonian however I am unable to get a result, this is my code:
import kwant
import tinyarray as ta
import numpy as np
import matplotlib.pyplot as plt
from tqdm import tqdm
import winsound
import os
from datetime import datetime
import scipy.sparse.linalg as sla
sig_0 = np.identity(4)
s_0 = np.identity(2)
s_z = np.array([[1., 0.], [0., -1.]])
s_x = np.array([[0., 1.], [1., 0.]])
s_y = np.array([[0., -1j], [1j, 0.]])
tau_z = ta.array(np.kron(s_z, s_0))
tau_x = ta.array(np.kron(s_x, s_0))
tau_y = ta.array(np.kron(s_y, s_0))
sig_z = ta.array(np.kron(s_0, s_z))
tau_zsig_x = ta.array(np.kron(s_z, s_x))
tau_zsig_y = ta.array(np.kron(s_z, s_y))
# Lorentzian definition
def lorentzianxy(x, y, ind,y0):
gam = 3
L = params["L"]
#if 0<ind<L:
return gam ** 2 /( gam ** 2 + (x - ind) ** 2 + (y - y0) ** 2)
# else :
# return 0
# Define potential
def potential(site, pot,ind,y0):
(x, y) = site.pos
return pot * lorentzianxy(x,y,ind,y0)
# Make system
def makeNISIN2D(params):
# List all the params
W=params["W"]
L=params["L"]
pot = params["pot"]
ind = params["ind"]
mu=params["mu"]
B=params["B"]
Delta=params["Delta"]
alpha=params["alpha"]
t=params["t"]
barrier = params["barrier"]
Smu = params["Smu"]
def lorentzianxy(x, y, ind,y0):
gam = 3
L = params["L"]
#if 0<ind<L:
return gam ** 2 /( gam ** 2 + (x - ind) ** 2 + (y - y0) ** 2)
# else :
# return 0
# Define potential
def potential(site, pot,ind,y0):
(x, y) = site.pos
return pot * lorentzianxy(x,y,ind,y0)
# if y < lorentzian(x,ind)*4:
#
# return (tru_pot)
# else:
# return 0
#
def Straightpotential(site, pot,ind):
(x, y) = site.pos
if x == ind:
return pot
else:
return 0
def onsiteSc(site, pot,ind,y0):
#(x,y)=site.pos
#L=params["L"]
# if x>L/2:
return (4 * t - Smu) * tau_z + B * sig_z + Delta * tau_x - potential(site, pot,ind,y0)*tau_z
# else:
#return (4 * t ) * tau_z + B * sig_z + Delta * tau_x - potential(site, pot,ind,y0)*tau_z
def onsiteNormal(site, pot,ind,y0):
return (4 * t - mu) * tau_z #- potential(site, pot,ind,y0)*tau_z
def onsiteBarrier(site, pot,ind,y0):
return (4 * t - mu + barrier) * tau_z #- potential(site, pot,ind,y0)*tau_z
def hop_x(site, pot, ind,y0):
return -t * tau_z + 0.5j * alpha * tau_zsig_y
def hop_y(site, pot, ind,y0):
return -t * tau_z - .5j * alpha * tau_zsig_x
# On each site, electron and hole orbitals.
lat = kwant.lattice.square(norbs=4)
syst = kwant.Builder()
# S
syst[(lat(i, j) for i in range(1,L-1) for j in range(W))] = onsiteSc
barrierLen = 1;
# I's
syst[(lat(i, j) for i in range(barrierLen) for j in range(W))] = onsiteBarrier
syst[(lat(i, j) for i in range(L-barrierLen, L)for j in range(W))] = onsiteBarrier
syst[kwant.builder.HoppingKind((1, 0), lat, lat)]= hop_x
syst[kwant.builder.HoppingKind((0, 1), lat, lat)]= hop_y
# N's
lead = kwant.Builder(kwant.TranslationalSymmetry((-1,0)),
conservation_law=-tau_z#, particle_hole=tau_y
)
lead[(lat(0, j) for j in range(W))] = onsiteNormal
lead[kwant.builder.HoppingKind((1, 0), lat, lat)]= hop_x
lead[kwant.builder.HoppingKind((0, 1), lat, lat)]= hop_y
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
return syst
def sorted_eigs(ev):
evals, evecs = ev
evals, evecs = map(np.array, zip(*sorted(zip(evals, evecs.transpose()))))
return evals, evecs.transpose()
params = dict(mu=0.3, Delta=.1, alpha=.8, t=1.0, barrier = 2.0, pot = 0.0,W = 5, L = 30, ind = 0, B = 0.3, Smu=0.00,y0=0)
sys = makeNISIN2D(params)
sys = sys.finalized()
# Calculate the wave functions in the system.
ham_mat = sys.hamiltonian_submatrix(sparse=True, params = params)
evals, evecs = sorted_eigs(sla.eigsh(ham_mat.tocsc(), k=20, sigma=0))
# Plot the probability density of the 10th eigenmode.
kwant.plotter.map(sys, np.abs(evecs[:, 9])**2,
colorbar=False, oversampling=1)
And the error I get is this: "ValueError: The number of sites doesn't match the number of provided values."
When I print the values they indeed are more than what they should be. I've tried a couple of things but I'm quite at a loss of what to do. I want to plot the wavefunction so I can see the Majoranas at the edges of the superconductor so that I can see how they respond to a local perturbation in the potential. Any tips would be very helpful.
Kind regards,
Hanifa
