Geometrically navigating topological platonic modes around gentle and sharp bends

TL;DR

This paper develops a predictive geometric theory to engineer topological-like effects in continuum systems, demonstrating the design of broadband, backscatter-resistant edge states in platonic crystals through symmetry and perturbation analysis.

Contribution

It introduces a first-principles approach to design topological edge states in continuum systems using geometric and symmetry considerations, bridging quantum and classical descriptions.

Findings

Design of broadband edge states resistant to backscatter

Identification of symmetry-induced Dirac cones and their gapping

Numerical validation of edge state behavior around bends

Abstract

Predictive theory to geometrically engineer devices and materials in continuum systems to have desired topological-like effects is developed here by bridging the gap between quantum and continuum mechanical descriptions. A platonic crystal, a bosonic-like system in the language of quantum mechanics, is shown to exhibit topological valley modes despite the system having no direct physical connection to quantum effects. We emphasise a predictive, first-principle, approach, the strength of which is demonstrated by the ability to design well-defined broadband edge states, resistant to backscatter, using geometric differences; the mechanism underlying energy transfer around gentle and sharp corners is described. Using perturbation methods and group theory, several distinct cases of symmetry-induced Dirac cones which when gapped yield non-trivial band-gaps are identified and classified. The propagative behavior of the edge states around gentle or sharp bends depends strongly upon the symmetry class of the bulk media and we illustrate this via numerical simulations.