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Today's Topics:

   1.  Transmission of each propagating mode (Lee Kwok-Long)
   2. Re:  Transmission of each propagating mode (Joseph Weston)


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Message: 1
Date: Fri, 6 Feb 2015 16:43:23 +0800
From: Lee Kwok-Long <kwoklonglee@gmail.com>
To: kwant-discuss@kwant-project.org
Subject: [Kwant] Transmission of each propagating mode
Message-ID:
        <CAMzfLzK0z7uFZGB54o71i8yr0hb2hf1D9GXxEhckubFYuQC5_g@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"

Dear all,
I want to calculate the transmission of each propagating mode separately,
but I do not know how the propagating modes are related to the scattering
matrix. For example, we can read from the bandstructure and find a mode at
E=0.2，kx=0.95pi, how to find the transmission for this mode. Or, we have
the transmission and how to find the contributions from each mode? Thanks
in advance!
Kwok-Long Lee
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Message: 2
Date: Fri, 06 Feb 2015 11:14:25 +0100
From: Joseph Weston <joseph.weston@cea.fr>
To: kwant-discuss@kwant-project.org
Subject: Re: [Kwant] Transmission of each propagating mode
Message-ID: <54D49401.70701@cea.fr>
Content-Type: text/plain; charset="utf-8"

On 06/02/15 09:43, Lee Kwok-Long wrote:
> Dear all,
> I want to calculate the transmission of each propagating mode
> separately, but I do not know how the propagating modes are related to
> the scattering matrix. For example, we can read from the bandstructure
> and find a mode at E=0.2，kx=0.95pi, how to find the transmission for
> this mode. Or, we have the transmission and how to find the
> contributions from each mode? Thanks in advance!
> Kwok-Long Lee

Hi,

I guess you are already familiar with the function `kwant.smatrix`
(http://kwant-project.org/doc/1.0/reference/generated/kwant.solvers.default.smatrix)
which allows you to obtain the full
scattering matrix for the problem. Once you have the full
scattering matrix you can obtain sub-blocks which pertain
to particular leads by using the `submatrix` method  of
the object returned by `kwant.smatrix`, and directly access the
scattering amplitudes between the different modes from this 2D array.
The documentation explains this better than I can
(kwant-project.org/doc/1.0/reference/generated/kwant.solvers.common.SMatrix),
however I will
try to illustrate what I mean with an example:

        sys = kwant.Builder()
        ... fill with sites, attach leads etc.
        fsys = sys.finalized()

        S = kwant.smatrix(fsys, energy=0.2)
        # scattering matrix between incoming modes in lead 0
        # and outgoing modes in lead 1
        S10 = S.submatrix(1, 0)
        # scattering amplitude between mode 2 in lead 0 and
        # mode 3 in lead 1
        S10[3, 2]

The mode numbering in the scattering submatrix matches the
mode numbering in the `lead_info` attribute of the object
returned by `kwant.smatrix`. This is again in the documentation
(kwant-project.org/doc/1.0/reference/generated/kwant.physics.PropagatingModes)

Hope that helps,

Joe




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