Two-dimensional Chern insulators: Expanding perspectives towards graphene


Appreciation from the twisted bilayer graphene community inspires topological-insulator researchers

Dr. Ozawa conducting research in his laboratory

Sometimes it pays to find out who is reading your work; unexpected attention can often expand ideas to new directions.

In a 2021 article, Ozawa and Mera from AIMR explored the relationship between the topology and the quantum metric—two measures that capture very different aspects—of two-dimensional Chern insulators1.

Using various Chern insulator models, the team found that the inequality relationship between the Chern number (topology) and the quantum volume (quantum metric) not only holds true, but it also approaches equality under certain conditions. Further, they determined that the condition for equality is related to the mathematical structure studied in the field of complex geometry called Kähler manifold2. These results were expected to address researchers interested in characterizing two-dimensional topological insulators.

However, after publication, the team found that the article was often cited by researchers working on the fractional quantum Hall (FQH) effect in twisted bilayer graphene (TBG).

“When we wrote the paper, we did not make the connection with the TBG system,” says Ozawa. “But seeing the interest from this specific community made us realize that the condition for inequality becoming equality might have direct implications on phenomena such as the TBG’s magic angle.”

In a follow-up article, the team related their results to the TBG system by introducing the concept of Kähler bands to describe topological insulators that satisfy the equality conditions, focusing on bands with constant curvatures that are conducive to FQH states.

“I am grateful for the unexpected appreciation from the TBG community,” says Ozawa. “It drew me into a new field, enabling me to expand my expertise to this day3.”

(Author: Patrick Han)


  1. Ozawa, T. & Mera, B. Relations between topology and the quantum metric for Chern insulators. Physical Review B 104, 045103 (2021). | article
  2. Mera, B. & Ozawa, T. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Physical Review B 104, 045104 (2021). | article
  3. Mera, B. & Ozawa, T. Uniqueness of Landau levels and their analogs with higher Chern numbers. arXiv:2304.00866 (2023). | article

This research highlight has been approved by the authors of the original article and all information and data contained within has been provided by said authors.