I am searching for a way to calculate the energy spectrum of a system without translational invariance using Kwant.
I am familiar with how to calculate E-k relationships for systems with translational invariance (such as a lead) using Kwant's infinite systems. What is unclear to me is how to approach doing this for a system which breaks this invariance, by for example,
applying an electric field via a gate or source-drain bias. In the tutorial section I have gone through the tutorial for calculating the magnetic flux vs. energy spectrum for a quantum dot, but it is unclear to me how one would modify this example to investigate
the E-k relationship.
I have seen a few examples of this type of calculation performed in the literature, but often the numerical details are left to the reader. A few of
these are below:
(1) http://arxiv.org/abs/cond-mat/0610237 - This paper shows several figures for differently shaped quantum wells formed along the transport direction in a graphene ribbon.
(2) http://arxiv.org/abs/1512.02144 - It appears to me that the lower panel of Fig. 1 essentially has an electric field, although I could be wrong. This example was actually done with Kwant.
(3) http://arxiv.org/abs/cond-mat/0603594 - Their Fig. 1 shows the spectrum in the quantum hall regime w/o an electric field applied (this I am able to reproduce w/Kwant). In their Fig. 2 an electric field
is applied in the x-direction of a graphene ribbon- this in particular I would like to be able to implement- in general, not necessarily for graphene.
I have attached a code I am working on which generates a square lattice ribbon with leads on the left/right sides. A potential well is formed in the ribbon in a similar fashion to (1) above. I can extract the Hamiltonian of the channel and calculate its
eigenvalues, but it is unclear to me how to get the E-k relationship. I believe I need to add some phase factor across the Hamiltonian which accounts for different k values.
I apologize if this is more of a physics question than a Kwant question. Indeed, Kwant trivializes what I imagine is the hard part- generating the lattice and turning that into a tight binding Hamiltonian. Hopefully this topic is of interest to the readers
of the mailing list- I believe it would be an interesting addition to the Kwant tutorials in the future!
Thanks so much!