Pseudo-magnetic Fields and Effective Dynamics in Strained Honeycomb Structures

TL;DR

This paper develops a mathematical framework to understand how strain-induced pseudo-magnetic fields influence wave packet dynamics in honeycomb structures, using spectral analysis to derive effective Dirac equations with gauge fields.

Contribution

It introduces a novel spectral analysis approach to control error terms and derive an effective Dirac equation governing wave dynamics in strained honeycomb media.

Findings

Effective approximation of wave packet dynamics by Dirac equations with gauge fields

Control of error terms in spectral analysis of strained media

Foundation for studying higher-order perturbations in honeycomb structures

Abstract

Strain offers a straightforward and effective method for generating pseudo-magnetic fields in optical and acoustic materials, thereby enabling precise manipulation of wave propagation. In this article, we investigate and justify wave packet dynamics localized near Dirac points in strained honeycomb-structured media. We develop a novel approach based on spectral analysis to control the error from second-order differential residue terms caused by the strain. The analysis yields a two-dimensional Dirac equation with nontrivial gauge fields governing the envelope dynamics, which is proved to well approximate the true solution in a long but finite time. These results contribute to the mathematical understanding of pseudo-magnetic effects in strained honeycomb structures and pave the way to systems with general higher-order perturbation terms.