# Example of 2D k-space models allowing interband transitions after a closed-loop trajectory? [closed]

I have been mainly exposed to 2D momentum-space condensed matter models in the context of Berry-related topology. I now want to study models where, if I take a closed loop in momentum space, I will have the possibility of an interband transition governed by selection rules. So far, all I have seen are charge-pumping-like effects with the Rice-Mele model (quantized flux pumping after one closed loop trajectory; example). I have seen some 2D models for excitons as well (example), but these don't consider a loop explicitly. Additionally, I understand that there is a perspective of potential virtual transitions associated with Berry curvature (due to its inherent interband character). However, I am looking for something more concrete than that.

I have read a bit about Landau-Zener transitions, but most works I have seen involve the time variable explicitly (example of selection rules). However, I am looking for an example of a model that studies interband transitions and selections rules in the context of a closed loop in k-space (very likely parameterized by parameter $$t$$: $$(k_x(t),k_y(t))$$. Since I have a ways to go in familiarizing myself with the field, I was hoping someone could suggest a resource that features such a model.

• I guess these would be non-adiabatic cases, and I have only been looking at adiabatic ones. Jul 8, 2021 at 14:38
• Or, if it is adiabatic, I think the trajectory should go through a gapless point... So, maybe this question might be hard to answer? Jul 13, 2021 at 7:32
• Hi TribalChief! Long time no chat! How did things go with this question? Did you find an answer? Aug 23, 2022 at 18:43
• This question appears to be abandoned. It can be reopened if OP returns and addresses questions/suggestions from the comments.
– Tyberius
Aug 23, 2022 at 22:16