Surface Solitons in Three Dimensions

TL;DR

This paper investigates the stability and existence of various localized surface modes, including solitons and vortices, in three-dimensional lattices, revealing that surfaces can enhance stability for certain structures.

Contribution

It provides new insights into how surfaces influence the stability and formation of complex localized modes in 3D lattices, including structures previously unstable in the bulk.

Findings

Surface extends stability regions for certain localized modes.

Three-site horseshoe is stable near the anti-continuum limit at the surface.

Vortices parallel to the surface exhibit increased stability regions.

Abstract

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site "horseshoe"-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anti-continuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface this increased stability region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.