Hi Leon,

“Tight binding” can have multiple meanings in this context, so I could use a little clarification.

 

The dispersion that I showed is already a tight-binding model in the sense that the spin example in the tutorial is a tight-binding model: I set up a lattice in kwant (kwant.lattice.chain in my case) and define the Cardona and Pollak Hamiltonian matrix at each site, and the momentum operators are turned into finite differences between the sites. I believe this is equivalent to using kwant’s continuum module.

 

The other meaning I can think of is to calculate the band structure using the tight-binding method directly in kwant: making a proper Si lattice in kwant, connecting the sites with the proper tight-binding matrix elements, etc. I’m sure that’s doable, but doing calculations with a 3D lattice sounds expensive.

 

What meaning of “tight-binding model” are you thinking of?

Do you have any ideas for how to make the modes that I don’t want become evanescent or otherwise get out of the energy range that I care about? The standard k.p method generates the band structure by perturbing free-particle electron states. As a consequence, at high enough ‘k’, all the modes look like parabolas, and I don’t think it’s possible to get the unwanted bands “out of the way”; the only way they can go is “up”. (I think that I’ve seen some funky k.p method that uses free-particle electron and “hole” states, so there are parabolas that face both up and down, which would allow a band-gap to exist even at large k. That could at least get the unwanted modes out of the band gap.)