What is it about?
In this paper we explore the phenomenon of flat bands in general periodic crystals, from a mathematical point of view. Flat bands are eigenvalues of the adjacency matrix for which there exist eigenfunctions of compact support, despite the periodic character of the model. Many results and open problems arise.
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Why is it important?
There has been intensive physics activity on this topic, but very few mathematical publications. This paper takes steps to explore this exciting problem and is an invitation to mathematicians to explore it further.
Perspectives
Classification of specific families of graphs is a natural perspective.
Mostafa Sabri
Read the Original
This page is a summary of: Flat bands of periodic graphs, Journal of Mathematical Physics, September 2023, American Institute of Physics,
DOI: 10.1063/5.0156336.
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