Number of Wavevectors for Each Frequency in a Periodic Structure

TL;DR

This paper analyzes the maximum number of wavevectors at each frequency in periodic structures, providing bounds and insights for material design and phonon dispersion modeling, including effects of non-local interactions.

Contribution

It introduces a method to determine the upper bound of wavevectors per frequency in general periodic structures, including damping effects, and applies it to phonon dispersion in Boron Nitride.

Findings

Upper bound for wavevectors per frequency established

First neighbor interactions are insufficient for accurate phonon dispersion modeling

Insights into non-local interactions in material design

Abstract

Periodic structures have interesting acoustic and vibration properties making them suitable for a wide variety of applications. In a periodic structure, the number of frequencies for each wavevector depends on the degree of freedom of the unit cell. In this paper, we investigate the number of wavevectors for each frequency. This analysis defines the upper bound for the maximum number of wavevectors for each frequency in a general periodic structure which might include damping. Investigation presented in this paper can also provide an insight for designing materials in which the interaction between unit cells is not limited to the closest neighbor. As an example application of this work, we investigate phonon dispersion curves in hexagonal form of Boron Nitride to show that first neighbor interaction is not sufficient to model dispersion curves with force-constant-model.