Semiclassical quantization conditions in strained moir\'e lattices

TL;DR

This paper extends semiclassical quantization rules to matrix-valued symbols with coalescing eigenvalues and applies this to analyze flat bands in strained moiré heterostructures, revealing new insights into their electronic properties.

Contribution

It generalizes the Bohr-Sommerfeld quantization condition to matrix symbols with eigenvalue coalescence, enabling analysis of flat bands in complex moiré systems.

Findings

Extended semiclassical quantization to matrix symbols with eigenvalue coalescence.

Applied the theory to strained moiré heterostructures to study flat bands.

Provided a mathematical framework for analyzing electronic states in complex lattices.

Abstract

In this article we generalize the Bohr-Sommerfeld rule for scalar symbols at a potential well to matrix-valued symbols having eigenvalues that may coalesce precisely at the bottom of the well. As an application, we study the existence of approximately flat bands in moir\'e heterostructures such as strained two-dimensional honeycomb lattices in a model recently introduced by Timmel and Mele.