Chambers's formula for the graphene and the Hou model with kagome periodicity and applications

TL;DR

This paper proves a Chambers-like formula for graphene and Hou models on kagome lattices, enabling semi-classical spectral analysis near flat bands, thus advancing understanding of their electronic properties.

Contribution

It establishes a new formula analogous to Chambers' for graphene and Hou models on kagome lattices, linking spectral properties across different lattice structures.

Findings

Derived a Chambers-like formula for kagome lattice models.

Performed semi-classical analysis of the spectrum near flat bands.

Connected spectral properties of graphene and Hou models.

Abstract

The aim of this article is to prove that for the graphene model like for a model considered by the physicist Hou on a kagome lattice, there exists a formula which is similar to the one obtained by Chambers for the Harper model. As an application, we propose a semi-classical analysis of the spectrum of the Hou butterfly near a flat band.