Second-order topological modes in two-dimensional continuous media

TL;DR

This paper introduces a symmetry-based method to realize second-order topological modes in continuous 2D media, demonstrating how pattern deformations can create localized in-gap states with potential for various experimental applications.

Contribution

The authors develop a novel scheme to generate 0D second-order topological modes in continuous 2D systems using symmetry and pattern deformation, supported by a quantitative topological analysis method.

Findings

Demonstrated creation of in-gap bound modes in hexagonal, Kagome, and honeycomb lattices.

Established a link between pattern deformation and the 2D Jackiw-Rossi model.

Provided a simulation-based method to optimize topological mode properties.

Abstract

We present a symmetry-based scheme to create 0D second-order topological modes in continuous 2D systems. We show that a metamaterial with a \textit{p6m}-symmetric pattern exhibits two Dirac cones, which can be gapped in two distinct ways by deforming the pattern. Combining the deformations in a single system then emulates the 2D Jackiw-Rossi model of a topological vortex, where 0D in-gap bound modes are guaranteed to exist. We exemplify our approach with simple hexagonal, Kagome and honeycomb lattices. We furthermore formulate a quantitative method to extract the topological properties from finite-element simulations, which facilitates further optimization of the bound mode characteristics. Our scheme enables the realization of second-order topology in a wide range of experimental systems.