Dear Olivier,
I see two options:
1) you can mix the two examples [1] [2] of kwant tutorial and work with a
quasi 1D system. In this case, you need to choose an energy for which you
will have only one conducting mode in the leads. You need also a spin orbit
coupling small enough to have a precession length much larger than the
width of your lead to avoid the non-parabolicity [3] in your dispersion
relation (ie: in order to obtain results close to the exact 1D system ).
So as you see, with this system, you can only study the non-adiabatic
situation of the article by Trushin and Chudnovskiy.
a small program is included below.
2) You can work with an exact 1D system (ie with a line ) . In this case,
you need to handle the circular part of your system.(kwant does not have a
lattice suitable for the cylindrical discritization )
The tip is to do the discritization of your Hamiltonian in the cylindrical
coordinates[4][5], then, you need to know that your discrete system is a
graph, and the position of the sites is not important anymore: only the
potential on the sites and the hoppings between them are pertinent. So you
will put the sites of your ring in a straight line and put the hoppings you
obtain from the discritization (the hoppings will be site dependent ) and
therefore you will finally get a simple 1D system that can be studied
by kwant.
You will need to use a hopping of the form : $-i\alpha \frac{\sigma_r}{R}$
with $\sigma_r= \sigma_x \cos(\theta)+\sigma_y \sin(\theta)$ [5]
(appendix)
#########################
from cmath import exp
from math import pi
import kwant
# For plotting
from matplotlib import pyplot
%matplotlib inline
import tinyarray
# define Pauli-matrices for convenience
sigma_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, t=1.0, W=10, r1=10, r2=20 ,alpha=0.5):
lat = kwant.lattice.square(a)
sys = kwant.Builder()
def ring(pos):
(x, y) = pos
rsq = x ** 2 + y ** 2
return (r1 ** 2 < rsq < r2 ** 2) and x>=0
sys[lat.shape(ring, (0, r1 + 1))] = 4 * t * sigma_0
sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
-t * sigma_0 - 1j * alpha * sigma_y
sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
-t * sigma_0 + 1j * alpha * sigma_x
sym_lead = kwant.TranslationalSymmetry((-a, 0))
def lead_shape(pos):
(x, y) = pos
return (r1 < abs(y) < r2)
def createLead(r):
lead=kwant.Builder(sym_lead)
lead[lat.shape(lead_shape, (0, r))] = 4 * t * sigma_0
lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
-t * sigma_0 - 1j * alpha * sigma_y
lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
-t * sigma_0 + 1j * alpha * sigma_x
return lead
lead1=createLead(r1+1)
lead2=createLead(-r1-1)
#### Attach the leads and return the system. ####
sys.attach_lead(lead1)
sys.attach_lead(lead2)
return sys
def main():
sys = make_system(alpha=.2)
# Check that the system looks as intended.
kwant.plot(sys)
# Finalize the system.
sys = sys.finalized()
data=[]
energies=[0.001*i for i in range(400)]
for energy in energies:
smatrix=kwant.smatrix(sys,energy)
data.append(smatrix.transmission(0,1))
pyplot.plot(energies,data)
if __name__ == '__main__':
main()
[1] nontrival shapes (kwant tutorial)
[2] Matrix structure of on-site and hopping elements Nontrivial shapes
(kwant tutorial )
[3]https://arxiv.org/pdf/0907.4122v1.pdf
[4]http://journals.aps.org/prb/abstract/10.1103/PhysRevB.70.195346
[5]http://skemman.is/stream/get/1946/10141/25310/1/ThesisMSc-CsabaD.pdf
--
I hope that this helps.
Adel
On Wed, Dec 7, 2016 at 6:22 PM, Oliver Generalao <
[email protected]> wrote:
> HI,
>
> I was trying to implement the paper
> http://link.springer.com/article/10.1134%2FS0021364006080042 in kwant,
> however I have trouble creating the geometry of the wire. I tried some
> tutorials, I got confused since I am a novice to kwant.
> It is a 3D setup with the wire(ideally close to a 1-D quantum wire) on
> xy-plane and the external field's direction is upward(in the direction
> of positive z-axis). The lead input is from x=-infinity to x=0(in the
> negative y-axis) ,then from x=0 the wire starts to curve(in a perfect
> semicircle manner) with radius R towards the positive y-axis, and the
> output lead starts from x=0 to x=-infinity.
>
> Herein is the figure attached as well.
>
> Any guidance and help in creating the code will be greatly
> appreciated. Thank you.
>
>
>
>
> --
> Oliver B. Generalao
>
> M.S. Physics student
> Structure and Dynamics Group
> National Institue of Physics
> University of the Philippines
> Diliman, Quezon City
> Trunkline: +63-2-981-8500
> Mobile: +63-927-4033966
>
--
Abbout Adel
