Thanks Joe! That was indeed the case! It became much closer with small a.

Best,

Ran

Hi Ran,

> I tried to compare KWANT’s results for transmission with Datta’s
ballistic transport formalism where total transmission is written as
>
> Ttot=T(E)M(E)
>
> Here Datta takes T(E)=1 for ballistic transport (please see: J. Appl.
Phys. 105, 034506, 2009) and M(E) is the number of modes in transverse
direction. When I compared KWANT's results with Datta’s expression,
for the system given in “quantum_wire_revisited.py”, I found different
results (please see the attached figure where I tried to put every
relevant thing in the calculation). Since the reflectance is zero for
that system and so transmission is 1 for each mode, shouldn’t it give
the same results with Datta’s transmission expression?
>

Nice question!

Looking at your results it seems that the energies at which new modes
open is shifted with respect to Datta's result.

I believe that this is simply due to the fact that your discretization
is not fine enough. Datta's result is valid in the continuum limit,
whereas the Kwant simulation (in the case presented) uses a
finite-difference discretization to render the problem discrete. If you
decrease the 'a' parameter, you should see the discrepancy between the
two result decrease.


Happy Kwanting,

Joe