Dear Leon,

I would tend to agree with Rafal and Joe: if your discretized k.p model has the correct dispersion relation in the energy window you are
interested it, every thing should be find. The only counter example I am aware of is fermion doubling with Dirac point, but Sillicon should be free of that.
As a sanity check, run a couple of simulations with different discretization parameters and check that you get the same answers.

Kind regards,
Xavier

Le 5 sept. 2017 à 23:45, Maurer, Leon <lmaurer@sandia.gov> a écrit :

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