Hi Luca,
> I have tried to implement a couple of examples of semimetals with Kwant, > where the lattices (scattering regions) are taken square or cubic, > and the leads attached on entire faces of the lattices. > I assumed both open and periodic (in the directions orthogonal to the leads) > boundaries conditions for the lattices and for the leads. I'm not sure what exactly you mean here. Could you post a code snippet that illustrates what precisely you mean? > Discussing at a conference, > I got aware vaguely about possible problems > that may arise when one wants to > discretize in real space an Hamiltonian originally written in > the space of momenta (also continuous). > This is exaclty what I have done always; > notice that I performed the discretization by hand, without > exploiting the routine in Kwant. > > Do you know about similar issues with semimetals ? > Do you have some advices ? So what you're saying is that you start with a continuum Hamiltonian and discretize it, correct? For certain classes of models this can certainly lead to unphysical states, even at energies where the continuum model is valid. For example, if we take a continuum model for graphene near a single dirac point so H∝|k|, discretize it with finite differences and diagonalize the resulting discrete Hamiltonian, we will see that the spectrum is proportional to sin(k)! This means that even at low energies (where the continuum model is valid) there are states close to k=π, which are *not* present in the continuum model, and that were introduced entirely as a result of the discretization. The general term for this is the "Fermion doubling problem". You should be able to tell if this is your issue by comparing the spectrum of the Kwant system with the spectrum of the continuum model from which it is derived. If you see that the "bands bend down" to give spurious states even at low energies then this could indicate that you have a Fermion doubling problem. You have to be more careful with the discretization to avoid the Fermion doubling problem, for example section B of https://arxiv.org/abs/0810.4787. I am not an expert in this field, so if it turns out that your problem *is* Fermion doubling, I would look into the relevant literature for that. Happy Kwanting, Joe
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