Macroscopic approximation of tight-binding models near spectral degeneracies and validity for wave packet propagation

TL;DR

This paper develops macroscopic models to accurately describe wave packet propagation near spectral degeneracies in tight-binding systems, with applications to graphene and validation through numerical simulations.

Contribution

It introduces a rigorous derivation of macroscopic approximations for wave packets near degeneracies in tight-binding models, extending their validity for complex materials like graphene.

Findings

Macroscopic models accurately approximate wave packets over long times near degeneracies.

The models are validated through numerical simulations of graphene systems.

The approach accounts for macroscopic variations such as shear and twist.

Abstract

This paper concerns the derivation and validity of macroscopic descriptions of wave packets supported in the vicinity of degenerate points $(K,E)$ in the dispersion relation of tight-binding models accounting for macroscopic variations. We show that such wave packets are well approximated over long times by macroscopic models with varying orders of accuracy. Our main applications are in the analysis of single- and multilayer graphene tight-binding Hamiltonians modeling macroscopic variations such as those generated by shear or twist. Numerical simulations illustrate the theoretical findings.