Dear Prof. Chan, > Dear Kwant developer, > Is it possible to combine the s matrices for two structures to obtain the s > matrix of a large system? The evanescent modes in a lead can be excited, does > the s matrix or some other object contain the evanescent mode information so > that it can be used for combining two s matrices?
Thanks for the interesting question! Indeed, it is not possible to naively combine s-matrices and also take into account the evanescent modes in the leads. Directly multiplying the smatrices for 2 systems would correspond to connecting them via an infinitely long lead. While the evanescent mode information is used when solving the scattering problem, this information is not kept around in the SMatrix object. Constructing the "extended" scattering matrix, which contains also the amplitudes of evanescent components, is possible but will get very technical. The best approach is perhaps that I give you some pointers as to where to look in the Kwant source code, and you post back in this thread when you have extra questions. Solving this would consist of 2 parts. The first part is modifying the calculation of the lead modes so that exponentially growing modes are also calculated (see most of [1], and specifically [2] for where the modes are identified). The second part involves hooking into the scattering solvers to correctly set up the linear system including the growing modes are computed, and selecting all the scattering amplitudes from the solution, including scattering into into evanscent modes. For starters you could look into the implementation of 'smatrix' [3] to see the general flow (setting up scattering problem as a linear system, identifying which parts of the solution to keep, and solving the linear system). Once you have the extended scattering matrix for each system you would then need to combine them via the scattering matrix for the "lead" connecting them. A precursor to the Kwant library had functionality for combining smatrices, which could be used as a starting point [4], however it does not contain the evanescent parts. Happy Kwanting, Joe [1]: https://gitlab.kwant-project.org/kwant/kwant/blob/master/kwant/physics/leads.py [2]: https://gitlab.kwant-project.org/kwant/kwant/blob/master/kwant/physics/leads.py#L465 [3]: https://gitlab.kwant-project.org/kwant/kwant/blob/master/kwant/solvers/common.py#L299 [4]: https://gitlab.com/meso/guts/blob/master/guts/sm.py#L373
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