Mechanism of phonon localized edge modes

TL;DR

This paper systematically investigates phonon localized edge modes, proposing two general conditions for their existence applicable across various lattice structures and potentials, enhancing understanding of vibrational localization at edges.

Contribution

It introduces two universal conditions for phonon localized edge modes, validated across multiple lattice types and interaction potentials, broadening the theoretical framework.

Findings

Two conditions are necessary for localized edge modes: inter-direction coupling and boundary condition differences.

The conditions are applicable to diverse lattice structures including 1D, 2D, and 3D systems.

The conditions hold for various interaction potentials such as valence force field and Brenner potential.

Abstract

The phonon localized edge modes are systematically studied, and two conditions are proposed for the existence of the localized edge modes: (I) coupling between different directions ($x$, $y$ or $z$) in the interaction; (II) different boundary conditions in three directions. The generality of these two conditions is illustrated by different lattice structures: one-dimensional (1D) chain, 2D square lattice, 2D graphene, 3D simple cubic lattice, 3D diamond structure, etc; and with different potentials: valence force field model, Brenner potential, etc.