Dear Khani,
I don't understand which comparaison are you talking about, but I can see
that you are not defining the angle theta correctly:
Theta is the angle made by the vector k and the x-axis so, it should be
k=sqrt(kx**2+ky**2)
Theta=180/pi *arcsin(kx/k)
You should notice that E= vf * |k|, so the expression you wrote is not
correct.
I hope this helps,
Adel
On Sun, Sep 6, 2020 at 12:23 PM Khani Hosein <hoseinkhani...@gmail.com>
wrote:
> Dear all,
> I want to calculate the transmission vs incident angle in graphene with a
> potential barrier. I use sys = kwant.wraparound.wraparound(sys) and lead
> = kwant.wraparound.wraparound(lead, keep=0) to construct the periodical
> system. I almost get the correct results, but I find that the definition of
> angle is different. Could you please help me to find out the reason. The
> results comparison is also attached.
> Regards,
> Khani Hosein
> my code is:
> import numpy as np
> import matplotlib.pyplot as plt
> from numpy import pi,sqrt
> import kwant
> import sys
> from numpy import pi
> from math import asin
> from matplotlib import pyplot
>
> a = 1.
> V0 = 0.0
> W = 2.
> L = 448
> t = 3
>
> def Rectangle(pos):
> x,y=pos
> return 0<=x<=L and -0.5<=y<=W
>
> sin_30, cos_30 = (1 / 2, sqrt(3) / 2)
> lat = kwant.lattice.general([(1, 0), (sin_30, cos_30)],
> [(0, 0), (1/2, 1 / (2*sqrt(3)))])
> a,b= lat.sublattices
>
>
> sys = kwant.Builder(kwant.TranslationalSymmetry(lat.vec((-1, 2))))
> sys[lat.shape(Rectangle,(0,0.6))]= 0.2
> sys[lat.neighbors(1)] = -t
> sys = kwant.wraparound.wraparound(sys)
>
> def lead_shape(pos):
> x,y=pos
> return -0.5<=y<=W
>
> lead = kwant.Builder(kwant.TranslationalSymmetry((1, 0), lat.vec((-1, 2))))
> lead[lat.shape(lead_shape,(0,0.6))] = 0.
> lead[lat.neighbors(1)] = -t
>
> lead = kwant.wraparound.wraparound(lead, keep=0)
> kwant.plot(sys)
>
> sys.attach_lead(lead)
> sys.attach_lead(lead.reversed())
>
> kwant.plot(sys)
> sys = sys.finalized()
>
> ky=0.
> momenta = [-2*pi + 0.002 * 2*pi * i for i in range(1001)]
> bands = kwant.physics.Bands(sys.leads[0],[ky])
> energies = [bands(k) for k in momenta]
>
> pyplot.figure()
> pyplot.plot(momenta, energies)
> pyplot.xlabel("momentum [(lattice constant)^-1]")
> pyplot.ylabel("energy [t]")
> pyplot.show()
>
>
> kys = np.arange(-0.08, 0.08, 0.0002)
> kysp =np.arange(-90, 90, 0.225)
> energy=0.08
> transmission = []
> num_prop = []
> thetap=[]
>
> for ky in kys:
> theta=180.*asin(ky/energy)/pi
> thetap.append(theta)
> smatrix = kwant.smatrix(sys, energy, [ky])
> transmission.append(smatrix.transmission(1, 0))
> num_prop.append(smatrix.num_propagating(0))
> print (ky)
>
> plt.plot(thetap, transmission)
> plt.show()
>
>
>
>
--
Abbout Adel
