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
Dear all,
sorry, this might be more a matplotlib question than a kwant question.
Below is a minimal code which produces two figures, each showing a different dataset: a current in the scattering region due to a wavefunction in a lead.
I would like to combine the two into a single plot, distinguishing the two datasets by e.g. different colormaps (and two different colorbars).
Any ideas?
Thanks a lot,
Tibor
______________________________________
import kwant
from math import pi, sqrt
from cmath import exp
import numpy
from matplotlib import pyplot as plt
#some parameters
t=1
L=30
W=30
EF=0.1
phi=0.01
def hopping(sitei, sitej, phi):
xi, yi = sitei.pos
xj, yj = sitej.pos
return -t*exp(1j*2*pi*phi*2/sqrt(3)*(yj - yi)*(xi + xj)/2)
def make_system():
lat = kwant.lattice.general([(sqrt(3)*1/2, 1/2), (0, 1)],
[(0, 0), (1/(2*sqrt(3)),1/2)], norbs=1)
def central_region(pos):
x, y = pos
return abs(x) < L/2 and abs(y) < W/2
def lead0_shape(pos):
x, y = pos
return abs(x) < L/2
#scattering region
sys = kwant.Builder()
sys[lat.shape(central_region, (0,0))] = -EF
sys[lat.neighbors()] = hopping
sys.eradicate_dangling()
#leads
sym = kwant.TranslationalSymmetry(lat.vec((0,1)))
lead0 = kwant.Builder(sym)
lead0[lat.shape(lead0_shape, (0,0))] = -EF
lead0[lat.neighbors()] = hopping
lead0.eradicate_dangling()
lead1=lead0.reversed()
return sys, lead0, lead1
sys, lead0, lead1 = make_system()
sys.attach_lead(lead0)
sys.attach_lead(lead1)
sysf = sys.finalized()
wf = kwant.wave_function(sysf, energy=0.0001, params=dict(phi=phi))
J = kwant.operator.Current(sysf)
psi1 = wf(0)[0]
e_current1 = J(psi1, params=dict(phi=phi))
psi2 = wf(1)[0]
e_current2 = J(psi2, params=dict(phi=phi))
kwant.plotter.current(sysf, e_current1, cmap="OrRd", colorbar=True, show=False)
ax = plt.gca()
plt.colorbar(ax.get_children()[-2], ax=ax)
kwant.plotter.current(sysf, e_current2, cmap="Blues", colorbar=True, show=False)
ax = plt.gca()
plt.colorbar(ax.get_children()[-2], ax=ax)
plt.show()
Dear Kwang users,
I have recently started using Kwant for making model Hamiltonian. It is really very good python package. I have started learning some tutorials. I would like to know if making tight-binding Hamiltonian with multi atom and multi orbital basis possible using Kwant. I can not find such example in documentation. I would like to then try to make a honeycomb lattice with two atoms and each atom with two basis, e.g., px, py.
Please help me to know about this in more detail.
Thanking you,
Santu B
Sent from my iPad
Hi all,
I am working on a spin resolved scattering problem using Kwant. The setup
is a simple heterojunction composed of normal metal and spin-orbit coupled
systems. I want to calculate the probabilities of spin-flipped and
spin-conserved reflection. In the normal metal, I use two lattices for
spin-up and spin-down states, and the calculation went well. The
probabilities for spin-flipped and spin-conserved reflection can be read
through inter- and intra-lattice scattering. Now I want to calculate the
scattering problem for an incident wave with spin polarization in the
x-direction.
My question: how to set the incident spin state along the x-direction and
calculate the corresponding spin-flipped (spin in -x direction) and
spin-conserved scattering probabilities?
Thanks very much!
Best,
Wei
--
College of Science, University of Aeronautics and Astronautics, Nanjing,
210016, P. R. China
E-mail: pchenweis(a)gmail.com <pchenweis(a)163.com>,
weichenphy(a)nuaa.edu.cn
Dear Sir,
Recently I was doing a problem on a 1D chain. The problem I faced is as
follows.
For a 1D chain, suppose I have taken 5 sites and set the hopping strength
between lead and system very small compared to the system hopping. Now
since we have 5 sites, from the Hamiltonian of the system we'll have 5
eigenvalues and if we calculate the transmission coefficient we shall have
5 peaks each occurs at particular eigenvalue.
But in my case, I am getting only three peaks. Am I missing something here?
Please help me. The following code I have used for the transmission
calculation.
#===================CODE==================
import kwant
# For plotting
from matplotlib import pyplot
import numpy as np
def make_system(a=1, t=1.0, L=5):
# Start with an empty tight-binding system and a single square lattice.
# `a` is the lattice constant (by default set to 1 for simplicity.
lat = kwant.lattice.chain(a)
syst = kwant.Builder()
#### Define the scattering region. ####
for x in range (L):
syst[(lat(x))] = 0
#syst[(lat(x) for x in range(L))] = onsite
syst[lat.neighbors()] = -t
#### Define and attach the leads. ####
lead = kwant.Builder(kwant.TranslationalSymmetry([-a]))
lead[(lat(0))] = 0
lead[lat.neighbors()] = -t
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())
#============== set hopping between lead and system ============
for i in syst.leads[0].interface:
for j in syst.neighbors(i):
syst[i,j] = 0.1
for i in syst.leads[1].interface:
for j in syst.neighbors(i):
syst[i,j] = 0.1
return syst
#================================================================
def main():
syst = make_system()
# Check that the system looks as intended.
kwant.plot(syst)
# Finalize the system.
syst = syst.finalized()
Es = np.linspace(-1.99, 1.99, 800)
data = []
totdos = []
for e in Es:
smatrix = kwant.smatrix(syst, e)
T = smatrix.transmission(1, 0)
ldos = kwant.ldos(syst, e)
totdos.append(sum(ldos)/len(ldos))
data.append(T)
print ('%0.3f' % e, '%.4f' % T, sum(ldos)/len(ldos))
pyplot.figure()
pyplot.plot(Es, data)
pyplot.xlabel("energy [t]")
pyplot.ylabel("conductance [e^2/h]")
pyplot.show()
# 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()
#================End CODE=======================
--
সুদিন
Hi All,
I am trying to plot V-I curves for graphene quantum dots but don't know how
to proceed. I have plotted conductance as a function of energy. Can anyone
help me understand how do I obtain V-I curves?
Any help will be much appreciated!
Thank you,
Sincerely,
Shivang
--
*Shivang Agarwal*
Junior Undergraduate
Discipline of Electrical Engineering
IIT Gandhinagar
Contact: +91-9869321451
Dear all Kwant workers!
My problem is about the calculation of energy dispersion of MoS2 in Ref PRB
92, 195402 (2015). I want to use the tight binding Hamiltonian of MoS2 (Eq
(2) in Reference)
to obtain energy dispersion in Figure 6(a). Because the honeycomb of
monolayer MoS2 is distinct with the graphene, onsite energy of Mo and S is
also different. In graphene,
the onsite energy of A and B atoms in unit cell is equivalent and thus the
hopping energy of nearest and two nearest atom in different direction is
same. However, this is not right
in MoS2 (A----Mo, B----S). So i choose the code to describe onsite energy in
MoS2 as follow
def onsite(site):
return E_M if (site.family == M) else E_X
Is this right?
Furthermore, i solve the energy band in y-direction by considering only one
lead (abs(y)<Ly, Ly is the width). Is it correct to use the following code
to build the system?
sym = kwant.TranslationalSymmetry(lat.vec((-1, 0)))
sys = kwant.Builder(sym)
My Kwant code cannot obtain the result in Figure 6(a).
Please help me if you are free, Thanks!
My Kwant code:
import kwant
from matplotlib import pyplot
import tinyarray
import math
import numpy
eV, nm=1,1e-9
lamad_M, lamad_X = 0.075*eV, 0.052*eV
e0, e2, ep, ez = -1.094*eV, -1.512*eV, -3.560*eV, -6.886*eV
V_pdd, V_pdp = 3.689*eV, -1.241*eV
V_ddd, V_ddp, V_ddde = -0.895*eV, 0.252*eV, 0.228*eV
V_ppd, V_ppp = 1.225*eV, -0.467*eV;
a0=0.316*nm;
s=1j;
sz=+1;
sqrt_3=math.sqrt(3)
E_M=tinyarray.array([[e0, 0, 0],[0, e2, -s*lamad_M*sz],[0, s*lamad_M*sz,
e2]]);
E_X=tinyarray.array([[ep+V_ppp, -s*lamad_X/2*sz, 0],[s*lamad_X/2*sz,
ep+V_ppp, 0],[0, 0, ez-V_ppd]]);
t1_MX=1/7*math.sqrt(2/7)*tinyarray.array([[-9*V_pdp+sqrt_3*V_pdd,
3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd],
[5*sqrt_3*V_pdp+3*V_pdd, 9*V_pdp-sqrt_3*V_pdd, -2*sqrt_3*V_pdp+3*V_pdd],
[-V_pdp-3*sqrt_3*V_pdd, 5*sqrt_3*V_pdp+3*V_pdd,
6*V_pdp-3*sqrt_3*V_pdd]])
t2_MX=1/7*math.sqrt(2/7)*tinyarray.array([[0, -6*sqrt_3*V_pdp+2*V_pdd,
12*V_pdp+sqrt_3*V_pdd],
[0, -6*V_pdp-4*sqrt_3*V_pdd, 4*sqrt_3*V_pdp-6*V_pdd],
[14*V_pdp, 0, 0]])
t3_MX=1/7*math.sqrt(2/7)*tinyarray.array([[9*V_pdp-sqrt_3*V_pdd,
3*sqrt_3*V_pdp-V_pdd, 12*V_pdp+sqrt_3*V_pdd],
[-5*sqrt_3*V_pdp-3*V_pdd, 9*V_pdp-sqrt_3*V_pdd,
-2*sqrt_3*V_pdp+3*V_pdd],
[-V_pdp-3*sqrt_3*V_pdd, -5*sqrt_3*V_pdp-3*V_pdd,
-6*V_pdp+3*sqrt_3*V_pdd]])
t1_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd),
-3/2*(V_ddde-V_ddd)],
[sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd),
sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)],
[-3/2*(V_ddde-V_ddd), sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd),
1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]])
t2_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3*(V_ddde-V_ddd), 0],
[sqrt_3*(V_ddde-V_ddd), V_ddde+3*V_ddd, 0],
[0 , 0,4*V_ddp]])
t3_MM=1/4*tinyarray.array([[3*V_ddde+V_ddd, sqrt_3/2*(-V_ddde+V_ddd),
3/2*(V_ddde-V_ddd)],
[sqrt_3/2*(-V_ddde+V_ddd), 1/4*(V_ddde+12*V_ddp+3*V_ddd),
-sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd)],
[3/2*(V_ddde-V_ddd), -sqrt_3/4*(V_ddde-4*V_ddp+3*V_ddd),
1/4*(3*V_ddde+4*V_ddp+9*V_ddd)]])
t1_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, sqrt_3*(V_ppp-V_ppd), 0],
[sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd,0],
[0, 0, 4*V_ppp]])
t2_XX=tinyarray.array([[V_ppd, 0, 0],
[0 ,V_ppp, 0],
[0, 0, V_ppp]])
t3_XX=1/4*tinyarray.array([[3*V_ppp+V_ppd, -sqrt_3*(V_ppp-V_ppd), 0],
[-sqrt_3*(V_ppp-V_ppd), V_ppp+3*V_ppd, 0],
[0, 0 ,4*V_ppp]])
lat = kwant.lattice.honeycomb()
M, X = lat.sublattices
def make_lead(Lx=1, Ly=48):
def Rectangle(pos):
x, y = pos
return abs(y)<Ly
def onsite(site):
return E_M if (site.family == M) else E_X
#sym = kwant.TranslationalSymmetry((-Lx, 0))
#sym = kwant.TranslationalSymmetry((-3, 0))
sym = kwant.TranslationalSymmetry(lat.vec((-1, 0)))
sys = kwant.Builder(sym)
#sys = kwant.Builder()
sys[lat.shape(Rectangle, (0, 0))] = onsite
#hopping_onsit_M=((0, 0),M,M)
#hopping_onsit_X=((0, 0),X,X)
#sys[kwant.builder.HoppingKind(*hopping_onsit_M)] = E_M##########
#sys[kwant.builder.HoppingKind(*hopping_onsit_X)] = E_X#########
hopping2_M =((1, 0), M, M)
hopping1_M =((-1, 1), M, M)
hopping3_M =((0, -1), M, M)
sys[kwant.builder.HoppingKind(*hopping1_M)] = t1_MM
sys[kwant.builder.HoppingKind(*hopping2_M)] = t2_MM
sys[kwant.builder.HoppingKind(*hopping3_M)] = t3_MM
hopping2_X =((1, 0), X, X)
hopping1_X =((-1, 1), X, X)
hopping3_X =((0, -1), X, X)
sys[kwant.builder.HoppingKind(*hopping1_X)] = t1_XX
sys[kwant.builder.HoppingKind(*hopping2_X)] = t2_XX
sys[kwant.builder.HoppingKind(*hopping3_X)] = t3_XX
hopping1_MX =((0, 0), M, X)
hopping2_MX =((0, 1), M, X)
hopping3_MX =((-1, 1), M, X)
sys[kwant.builder.HoppingKind(*hopping1_MX)] = t1_MX
sys[kwant.builder.HoppingKind(*hopping2_MX)] = t2_MX
sys[kwant.builder.HoppingKind(*hopping3_MX)] = t3_MX
def family_colors(site):
return 0 if (site.family == M) else 1
def hopping_lw(site1, site2):
return 0.05 if site1.family == site2.family else 0.1
def hopping_color(site1,site2):
return 'g' if site1.family==site2.family else 'b'
kwant.plot(sys,site_color=family_colors,site_lw=0.05,
hop_lw=hopping_lw,hop_color=hopping_color,colorbar=False)
return sys
def main():
lead = make_lead().finalized()
kwant.plotter.bands(lead, show=False)
pyplot.xlabel("momentum [(lattice constant)^-1]")
pyplot.ylabel("energy [eV]")
pyplot.show()
# 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()
