Dear Kwant community,
I am a physics student and I am approaching to Kwant to solve simple
problems of scattering.
I am new in Kwant and, for this reason, I'm trying to use Kwnat for basic
problems of scattering.
The most simple problem in my mind is the scattering of a plane-wave (1
dimension) from the left of a potential barrier. If we now suppose the
potential barrier is 'zero' everywhere, the scattering matrix, according to
the scattering theory, should be 'S={{0,1},{1,0}}'.
If I try to compute the reflection and transmission coefficient, I obtained
the correct values (1 for reflection and 0 for transmission). But it occurs
only for some energies. For example in the code I attached, if I put the
value of '10' in 'S=kwant.solvers.default.smatrix(syst,10)' I obtaine for
reflection and transmission the value of '0'. Where is my errors? And, is
there a way to print the entire elements of the scattering matrix ?
Yours sincerely
Lorenzo Bagnasacco
#!/usr/bin/env python
# coding: utf-8
# In[1]:
get_ipython().system('pip install kwant')
get_ipython().system('pip install SymPy')
# In[2]:
import kwant
from matplotlib import pyplot
import numpy as np
import kwant.continuum
import math
# In[3]:
template1 = kwant.continuum.discretize('k_x * k_x')
print(template1)
# In[4]:
syst = kwant.Builder()
# In[5]:
a=1
lat=kwant.lattice.square(a)
# In[6]:
t=1
leng=20
# In[7]:
for i in range(leng):
#On-site Hamiltonian
syst[lat(i,0)] = 2 * t
#Hopping in x-direction
if i > 0:
syst[lat(i,0),lat(i-1,0)] = - t
# In[8]:
kwant.plot(syst);
# In[9]:
sym_left_lead = kwant.TranslationalSymmetry((-a,0))
left_lead=kwant.Builder(sym_left_lead)
left_lead[lat(-1,0)]= 2 * t
left_lead[lat(-1,0),lat(0,0)]= - t
# In[10]:
kwant.plot(left_lead);
# In[11]:
syst.attach_lead(left_lead)
kwant.plot(syst);
# In[12]:
sym_right_lead = kwant.TranslationalSymmetry((a,0))
right_lead=kwant.Builder(sym_right_lead)
right_lead[lat(leng,0)]= 2 * t
right_lead[lat(leng,0),lat(leng-1,0)]= - t
# In[13]:
kwant.plot(right_lead);
# In[14]:
syst.attach_lead(right_lead)
kwant.plot(syst);
# In[15]:
syst=syst.finalized()
# In[20]:
S=kwant.solvers.default.smatrix(syst,10)
# In[21]:
trans = []
refl = []
trans.append(S.transmission(1, 0))
refl.append(S.transmission(0, 0))
# In[22]:
trans
# In[23]:
refl
# In[ ]:
