Thanks a lot for clarifying my doubts, just first I wanted to observed deformation and now I will be trying to incorporate hopping parametrization. Regards, Shrushti
On Fri, Jul 23, 2021 at 3:32 PM Adel Belayadi <adelp...@gmail.com> wrote: > Dear Shrushti, > > From a tight binding point of view, once we have defined our lattice and > shape, we need to care about the hopping and on-site energy, not the > positions. In your case and in order to parameterise the hopping in the > strained region you need to know the position transforms. In fact, > parameterizing the hopping is the most important task. In strained > graphene, parameterising the hopping is somehow similar to adding a > magnetic field in the system. > > *In your script you have written: syst=pos_transform((5,0),0.05,pi/2)* > > This is completely wrong and Kwant will not be able to recognize the > system. Since you are recently discovering Kwant, I recommend you to go > through Kwant FAQ: https://kwant-project.org/doc/dev/tutorial/faq > > Back to your issue, I guess you are caring to see the strained shape. In > this case, you need to use pos_transorm like: > *kwant.plot(syst, pos_transform=lambda pos: > pos_transform(pos,c=c,angle=angle), * > > Just one more thing, donot forget to uncommenthoppings = (((0, 0), a, b), > ((0, 1), a, b), ((-1, 1), a, b))syst[[kwant.builder.HoppingKind(*hopping) for > hopping in hoppings]] = totherwise you will not be able to see the strained > position. > > Finally, you need to focus on using the correct hopping BestAdel > > > > Le jeu. 22 juil. 2021 à 09:48, Shrushti Tapar <shrushti.tapa...@gmail.com> > a écrit : > >> 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 <adelp...@gmail.com> 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/kwant-discuss@kwant-project.org/msg00574.html >>> >>> I hop this will help >>> Best wishes >>> >>> Le jeu. 15 juil. 2021 à 14:19, <shrushti.tapa...@gmail.com> 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 >>>> >>>
