Position dependent effective mass by discretization interface.
Dear all, I am using Kwant to discretize an effective mass approximation scheme. Efforts to implement position dependent effective mass to model a metal-semiconductor hetrojunction have so far been futile. To avoid having to discretize the entire system with the high accuacy needed in the metal parts (the leads) i want to have different discretisation in different parts of the system. So my question is if it is possible to have such an interface between discretizations and if so, how could it be implemented in Kwant? Thank you in advance. Emil Johansson PS: Have tried the straight on approach with having a polyatomic lattice and in one part only having one of the monoatomic sublattices present. This however do no generate results in agreement with analytical results for a simple 2D wire test system. Attached a plot of the test system.
Hi Emil, I'm just making a guess here, but I imagine you'd need to connect all boundary sites of one lattice to all boundary sites of the other. Not sure what to take for the coupling strengths though. Best, Anton On Mon, Apr 18, 2016 at 9:33 AM, Emil Johansson <emil.sweden@gmail.com> wrote:
Dear all,
I am using Kwant to discretize an effective mass approximation scheme. Efforts to implement position dependent effective mass to model a metal-semiconductor hetrojunction have so far been futile. To avoid having to discretize the entire system with the high accuacy needed in the metal parts (the leads) i want to have different discretisation in different parts of the system.
So my question is if it is possible to have such an interface between discretizations and if so, how could it be implemented in Kwant?
Thank you in advance.
Emil Johansson
PS: Have tried the straight on approach with having a polyatomic lattice and in one part only having one of the monoatomic sublattices present. This however do no generate results in agreement with analytical results for a simple 2D wire test system. Attached a plot of the test system.
Hi, I think there will probably be some interplay between physical effects (due to the abrupt interface between two materials with different effective masses) and artificial effects (due to the discretization of the model). It would not surprise me that you get unphysical effects for sufficiently high energies/short wavelengths ("high" to be defined ;)) because then you will be probing the differences between the discretization schemes used. I would certainly start by using a single discretization scheme and checking that you get the results you expect. If I understand correctly you are only trying to use different discretization schemes for performance reasons, so on a practical level I would also suggest looking at whether the extra hassle of using different discretization schemes is worth the gain in speed. Happy Kwanting, Joe
Hi again, A colleague just pointed out this article [1] where they use different discretization schemes. I believe that your question is sufficiently broad (try "nonuniform finite differences" as a search term) that this will have been addressed in other publications too. Happy Kwanting, Joe [1]: http://scitation.aip.org/content/aip/journal/jap/68/8/10.1063/1.346245
participants (3)
-
Anton Akhmerov -
Emil Johansson -
Joseph Weston