Dear Adel Belayadi,
I am new to Kwant, as per our previous discussion, here I am attaching my
program, I have defined my strain region and function for uniaxial strain
in armchair direction. Now I struggling with *how to introduce this
function* in the program. Please correct me if I have understood it
wrongly, Firstly we have to define graphene, by using the position of
lattice points we have to apply pos_transform in a specified region, which
will use the values of x and y co-ordinate from lattice placement due to
lattice structure. The next doubt is like, as I using uniaxial strain in Y
direction, it will squeeze lattice in X direction. So, the unstrained
lattice point also has to shift accordingly. Right now I am only focusing
on position displacement and not hopping.
import numpy as np
import scipy.io as spio
from numpy import *
import scipy.linalg as la
import matplotlib as mpl
import sympy as sym
import kwant
#%%######################
# parameters
L=20 # Length of device on both sides
W=5 # Width of device
t=-2.7
pot=0.5
c=0.05
angle=pi/2
# lattice type
graphene = kwant.lattice.general([(1, 0), (sin(pi/6), cos(pi/6))],
[(0, 0), (0, 1 / sqrt(3))],
norbs=1)
a, b = graphene.sublattices
# scattering region
def rectangle(pos):
x, y = pos
return 0 <= x <= L and 0<= y <= W
# strain_pos
def pos_transform(pos,c,angle):
x,y= pos
if 5<x<10:
ux=(cos(angle)**2-0.165*sin(angle)**2)*c*x
uy=(sin(angle)**2-0.165*cos(angle)**2)*c*y
return x+ux,y+uy
else:
return x,y
syst = kwant.Builder()
syst[graphene.shape(rectangle, (0, 0))] = 0
syst=pos_transform((5,0),0.05,pi/2)
#hoppings = (((0, 0), a, b), ((0, 1), a, b), ((-1, 1), a, b))
#syst[[kwant.builder.HoppingKind(*hopping) for hopping in hoppings]] = t
kwant.plot(syst);
Thanks in advance.
Regards,
shrushti
On Fri, Jul 16, 2021 at 2:38 AM Adel Belayadi <[email protected]> wrote:
> Dear Shrushti,
> it is straightforward to deal with strained graphene.
> In the region you want to make strain, just set the function which
> modifies the site position (this mainly depends on the amount and type of
> the strain). Second, once you have shifted the site position you need to
> shift the hopping as illustrated in the file provided by Mr. Antonio.
> here you find a simple script about how to shift the site position in the
> case of uniaxial strain (adjusted to you case)
>
> def Triaxial_transform(pos, center, I):
> """ I is a parameter that lets us to control the intensity of the
> strain"""
> x, y = pos
> cx, cy = center[0], center[1] # the center of the strain
> r=sqrt((x-cx)**2+(y-cy)**2)
> if r<sigma:
> ux = 2*I * x*y
> uy = I * (x**2 - y**2)
> return x + ux, y + uy
> else:
> return x, y
>
> Then use this position to set your hopping as illustrated in a previous
> discussion [Ref-1].
>
> You have to be careful in case you are using a strain in the z axis since
> you will not be able to plot the current. It is somehow tricky in this
> scenario.
>
> [Ref-1]
> https://www.mail-archive.com/[email protected]/msg00574.html
>
> I hop this will help
> Best wishes
>
> Le jeu. 15 juil. 2021 à 14:19, <[email protected]> a écrit :
>
>> I want to create the graphene strained superlattice-like structure,
>> having uniaxial strain defined at the specified region. Please, someone can
>> suggest to me how to define the strained region and interface between
>> unstrained and strained graphene regions.
>> Thanks in Advance
>> Shrushti
>>
>
