Dear Adel,
At first I thought that we can make scattering region and then attached it to
the lead. But now I understant that scattering region depends on the symetry
vector. Am I right?
Please look at my code:
import kwant
from math import sqrt
import matplotlib.pyplot as plt
import tinyarray
import numpy as np
import math
import cmath
#import scipy.linalg as la
import matplotlib
d=1.42;
a1=d*math.sqrt(3);
#on-site energy...................................................
t=-3.033;
latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)],
[(a1/2,-d/2),(a1/2,d/2)])
a,b = latt.sublattices
syst= kwant.Builder()
#...................................................................................
def rectangle(pos):
x, y = pos
z=x**2+y**2
return -2.9*a1<x<2.9*a1 and -7.5*d<y<7.5*d
syst[latt.shape(rectangle, (1,1))]=0
def delet(pos):
x, y = pos
z=x**2+y**2
return z<(1*a1)**2
del syst[latt.shape(delet, (1,1))]
#nearest neighbors.............................................................
syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t
syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t
syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t
ax=kwant.plot(syst);
ax.savefig('syst1.pdf')
sym = kwant.TranslationalSymmetry(latt.vec((-4,0)))
sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)])
sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)])
lead = kwant.Builder(sym)
def lead_shape(pos):
x, y = pos
return -7.5*d<y<7.5*d
lead[latt.shape(lead_shape, (1,1))] = 0
def delet_lead(pos):
x, y = pos
z=x**2+y**2
return z<(1*a1)**2
del lead[latt.shape(delet_lead, (1,1))]
lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t
lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t
lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t
syst.attach_lead(lead,add_cells=0)
syst.attach_lead(lead.reversed(),add_cells=0)
ax=kwant.plot(syst);
ax.savefig('syst.pdf')
fsys = syst.finalized()
Sites= list(fsys.sites) #list of all the sites in the scattering region
number_of_sites=len(Sites)
In the above-mentioned code, the line with green color is a shape we constructe
as scattering region and the line with pink color is a shape that kwant
constructe according to the symmetry vector and attached leads. When we look at
to the both shapes and also the number of their sites (they are saved as pdf
format) the scattering region made by us is different by scattering region made
by kwant (with lead). Is there any way that both scattering regions will be
same?
according to the
fsys = syst.finalized()
Sites= list(fsys.sites) #list of all the sites in the scattering region
number_of_sites=len(Sites)
kwant code gives us the number of sites of the scattering region in terms of
the line with pink color. I need in the scattering region just have one hole
like in the shape according to the line with green color.
That is very kind of you if you help me.
Best,
Sajad
From: "Abbout Adel" <[email protected]>
To: "Saj.ZiaBorujeni" <[email protected]>
Cc: "kwant-discuss" <[email protected]>
Sent: Monday, Azar 11, 1398 10:57:27 AM
Subject: Re: [Kwant] Access to eigenvalue, eigenvector and number of points in
each unit cell
Dear Sajjad,
The documentation of kwant is very rich and explains all these requirements
with multiple examples. Please have a thorough look at those examples.
The requested code is below.
I hope this helps,
Adel
import kwant
from numpy import *
lat=kwant.lattice.square()
sys=kwant.Builder()
def pot(site, V):
return V
sys[(lat(x,y) for x in range(5) for y in range(5))]=pot
sys[lat.neighbors()]=-1
sym_lead = kwant.TranslationalSymmetry((-1, 0))
lead = kwant.Builder(sym_lead)
lead[(lat(0,y) for y in range(5))]=0
lead[lat.neighbors()]=-1
sys.attach_lead(lead)
kwant.plot(sys)
sysf=sys.finalized()
Sites=list(sysf.sites)
Sites_pos=[site.pos for site in Sites] #getting the positions for example
H=sysf.hamiltonian_submatrix(params=dict(V=5))
On Mon, Dec 2, 2019 at 9:41 AM Saj.ZiaBorujeni <
[email protected] > wrote:
Dear Adel,
Thank you for your response. I am trying to use your Instructions for finding
all site in the scattering region and also finding eigenvalu but I can not.
That is very kind of you if you send me a short example of these problem. Would
you please?
Best regard
Sajad
From: "Abbout Adel" < [email protected] >
To: "Saj.ZiaBorujeni" < [email protected] >
Cc: "kwant-discuss" < [email protected] >
Sent: Saturday, Azar 2, 1398 7:21:58 PM
Subject: Re: [Kwant] Access to eigenvalue, eigenvector and number of points in
each unit cell
Dear Sajad,
Getting the number of sites in the central system is easy in kwant.
sysf= syst.finalized()
Sites= list(sysf.sites) #list of all the sites in the scattering region
number_of_sites=len(Sites).
Getting the Hamiltonian of the central system is also straightforward:
H=sysf.hamiltonian_submatrix()
I want just to stress that the eigenvalues of this Hamiltonian have nothing to
do with the band structure. In fact, to get the band structure, you need the
hamiltonian H0 of the unit cell in the lead and the hopping matrix V between
two unit cells. With the help of the Bloch theorem, the band can be obtained by
diagonalizing:
H0+V*exp(+ik)+V^\dagger *exp(-ik) for all your k points.
ps: (H and H0 may be different depending on how you define your system!)
I hope this helps.
Adel
On Sat, Nov 23, 2019 at 1:09 AM Saj.ZiaBorujeni <
[email protected] > wrote:
Dear Joseph Weston,
yes you are right.
"I am trying to create a system with translational symmetry, and that each
Kwant *site* corresponds to a single atom."
We know according to the nanoribbon, we have a scattering region that is
attached to the leads. I want to find the number of kwant site (which I
mentioned as atom) in the scattering region (which I mentioned as unit cell).
Please look at the following example for the graphene nanoribbon:
import kwant
from math import sqrt
import matplotlib.pyplot as plt
import tinyarray
import numpy as np
import math
import cmath
import matplotlib
d=1.42;
a1=d*math.sqrt(3)
t=-3.033;
latt = kwant.lattice.general([(a1,0),(a1*0.5,a1*math.sqrt(3)/2)],
[(a1/2,-d/2),(a1/2,d/2)])
a,b = latt.sublattices
syst= kwant.Builder()
#...................................................................................
def rectangle(pos):
x, y = pos
z=x**2+y**2
return -2.9*a1<x<2.9*a1 and -7.5*d<y<7.5*d
syst[latt.shape(rectangle, (1,1))]=0
syst[[kwant.builder.HoppingKind((0,0),a,b)]] =t
syst[[kwant.builder.HoppingKind((0,1),a,b)]] =t
syst[[kwant.builder.HoppingKind((-1,1),a,b)]] =t
ax=kwant.plot(syst);
sym = kwant.TranslationalSymmetry(latt.vec((-5,0)))
sym.add_site_family(latt.sublattices[0], other_vectors=[(-1, 2)])
sym.add_site_family(latt.sublattices[1], other_vectors=[(-1, 2)])
lead = kwant.Builder(sym)
def lead_shape(pos):
x, y = pos
return -7.5*d<y<7.5*d
lead[latt.shape(lead_shape, (1,1))] = 0
lead[[kwant.builder.HoppingKind((0,0),a,b)]] =t
lead[[kwant.builder.HoppingKind((0,1),a,b)]] =t
lead[[kwant.builder.HoppingKind((-1,1),a,b)]] =t
syst.attach_lead(lead,add_cells=0)
syst.attach_lead(lead.reversed(),add_cells=0)
ax=kwant.plot(syst);
def plot_bands(syst):
fsys = syst.finalized()
plt.figure()
kwant.plotter.bands(fsys.leads[0], args=(dict(gamma=1., ep=0.),))
plt.xlabel("K")
plt.ylabel("band structure (eV)")
plt.ylim((-4.0,4.0))
plt.show()
plot_bands(syst)
Here we have a main region such that the whole system can be made by repeating
this region. I want to know the number of site in the main region.
"It is not 100% clear to me what you want when you say "the eigenvectors and
eigenvalue" of your Hamiltonian; if your system has translational symmetry then
presumably you want the eigen-decomposition *at a given quasi-momentum*, but
you do not explicitly state this, so I am not sure."
When we plot the band structure, we have a Hamiltonian (the dimension is N*N)
in terms of K point. So, we have N eigenvalues for each K point. How we can
find these eigenvalues for each K point. How is it shown in Kwant? Would you
please help me.
Best,
Sajad
From: "Joseph Weston" < [email protected] >
To: "Saj.ZiaBorujeni" < [email protected] >,
[email protected]
Sent: Thursday, Aban 30, 1398 3:59:57 PM
Subject: Re: [Kwant] Access to eigenvalue, eigenvector and number of points in
each unit cell
Hi Sajad,
Dear all,
I need to access to the number of atoms of my unit cell, the eigenvalue and
eigenvectors for each eigenvalue of my Hamiltonian.
Is there any one to help me and let me know if it is possible in kwan to access
them.
Could you post a short code example showing what you are doing? You refer to
"atoms" and "unit cell", so I presume that you are trying to create a system
with translational symmetry, and that each Kwant *site* corresponds to a single
atom.
It is not 100% clear to me what you want when you say "the eigenvectors and
eigenvalue" of your Hamiltonian; if your system has translational symmetry then
presumably you want the eigen-decomposition *at a given quasi-momentum*, but
you do not explicitly state this, so I am not sure.
Posting a complete code example is useful because it is more precise than
describing your problem with words.
Happy Kwanting,
Joe
--
Abbout Adel
--
Abbout Adel
