p-orbital disclination states in non-Euclidean geometries

TL;DR

This paper demonstrates that disclinations in non-Euclidean geometries of 2D materials can host topologically protected acoustic modes, combining experimental and theoretical approaches to explore new topological phenomena.

Contribution

It introduces the first experimental realization of topological bound states induced by disclinations in non-Euclidean geometries within acoustic systems.

Findings

Disclinations create topologically protected bound modes.

Non-Euclidean geometry influences p-orbital band topology.

Experimental and simulation results are consistent.

Abstract

Disclinations are ubiquitous lattice defects existing in almost all crystalline materials. In two-dimensional nanomaterials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries. However, such geometries have never been investigated experimentally in the context of topological phenomena. Here, by creating the physical realization of disclinations in conical and saddle-shaped acoustic systems, we demonstrate that disclinations can lead to topologically protected bound modes in non-Euclidean surfaces. In the designed honeycomb sonic crystal for p-orbital acoustic waves, non-Euclidean geometry interplay with the p-orbital physics and the band topology, showing intriguing emergent features as confirmed by consistent experiments and simulations. Our study opens a pathway towards topological phenomena in non-Euclidean geometries that may inspire future studies on, e.g., electrons and phonons in nanomaterials with curved surfaces.