Hi Joe,

And how can I set lead1's potential correctly? What is wrong in my script zigzag.py? I have the same function onsite both for scattering region and for leads:

    def potential( site, _U ):
        x, y = site.pos
        return _U if x >= 0 else 0

    def onsite( site, _U=0 ):
        return eps + potential( site, _U )

    syst = kwant.Builder()

    syst[graphene.shape(stripe, (0,0))] = onsite

***
    sym1 = kwant.TranslationalSymmetry(graphene.vec((2, -1)))
    def lead1_shape(pos):
        x, y = pos
        return abs(y) <= 0.5*_W

    lead1 = kwant.Builder(sym1)
    lead1[graphene.shape(lead1_shape, (0, 0))] = onsite

Sincerely,
Jambulat

2017-03-29 12:06 GMT+03:00 Joseph Weston <joseph.weston08@gmail.com>:
Hi,

> Joe, great thanks for Your explaination. It would be quite hard for me to
> understand from the code documentation that it is the submatrix method is
> the thing which I need. But could You say is the function below calculates
> averaged over all modes transparency adequately?
>
> tblock = smatrix.submatrix( 1, 0 )
>
> def transparency( tblock ):
>     return ( 0 if tblock.shape[0] == 0 else
>              np.sum( np.abs( tblock )**2 )/tblock.shape[0] )

Seems correct

> I want to use it to check the results obtained analytically in the case of
> the wave falling on a potential barrier in infinite graphene. But now I see
> that 'transparency' depends on the length of the scattering region L
> despite of that the scattering is expected only at the line x=0. What
> should I do for obtaining more reliable results, to leave only one-two unit
> cells inside scattering region, or maybe make scattering region more long?
> Also it's a bit strange that 'transparency' is zero for potential barriers
> higher than scattering energy for the case of quite wide nanoribbons
> (W=100nm). According to theory, if I'm not mistaken, electron at any case
> is able to pass through a barrier in graphene, when the barrier is higher
> than its energy, electron just becomes a hole. In some sense this is
> approved by experiment, conductivity of the graphene FET saturates with
> increasing of gate voltage (e.g. see
> http://pubs.acs.org/doi/abs/10.1021/nl204088b ). But doing the similar
> simulations in Kwant I obtain conductivity cut-off for big voltages. You
> can see the graphs here:
> https://preview.ibb.co/crtEFa/graphene.png
> https://ibb.co/jZr1va (better resolution)
> I'm also attaching the scripts which have generated this graphs, but I'm
> not certain that they are not be banned. But it would be great if You check
> them and find that I did there something wrong.

In your 'zigzag.py' script you apply potential for all x >= 0 in the
scattering region (in both the left and the right leads there is a 0
potential). As you increase L, you increase the length of the
barrier so it does not surprise me that the transmission drops to 0.

Happy Kwanting,

Joe