Hi all,
After my failure with k.p, I successfully used Kwant to implement a tight binding model of Si’s band structure -- specifically the first nearest-neighbor sp3s* model of Vogl et al., J. Phys. Chem Sol. 44, 365 (1983). I’ve attached a rough implementation (jupyter notebook attached – just run all).
I’d appreciate any feedback about how to simplify the Kwant part of the code (especially setting up the lattice, adding hopping terms, etc.). The nitty-gritty parts of kwant are new to me.
Anyhow, I’ll probably have questions in the near future about how to integrate this model into structures with leads and other translational symmetries (specifically, with structures that don’t have translational symmetries in the directions of the Si primitive vectors).
-Leon
From: "Maurer, Leon"
Date: Tuesday, September 5, 2017 at 3:45 PM
To: "kwant-discuss@kwant-project.org"
Subject: Re: [Kwant] [EXTERNAL] Re: beyond effective mass (limiting kwant to a range of k)
Hi Joe,
I personally don't really have any experience with k.p models, so I don't think I will be much help; hopefully someone else on the mailing list will be better able to. That being said, these high-k modes are surely present even in the continuum, no? They are a consequence of the k.p model you are using, *not* the discretization, so I would agree with what Rafal said: that you need to make sure your model is valid at the energies you care about first before discretizing.
I see what you’re saying. Yes, The high-k modes are present in the continuum; they’re just ignored because they’re outside the Brillouin zone.
The idea of adding "dummy" degrees of freedom and a coupling to open up a gap seems reasonable. You could also just calculate the scattering matrix *with* the high-k modes included and see whether there is any scattering to/from the low-k modes. If there's not you might be able to get away with not doing anything about them at all?
I was also wondering if there was much coupling between the high- and low-k modes. How would I extract that info from the scattering matrix?
Thanks.
-Leon
