Dirac cones and higher-order topology in quasi-continuous media

TL;DR

This paper explores Dirac cones and higher-order topological phases in quasi-continuous classical wave media, demonstrating tunable topological features in sonic crystals and providing a comprehensive theoretical framework.

Contribution

It introduces a unified framework for understanding Dirac cones and higher-order topology in classical wave systems, with practical examples in sonic crystals.

Findings

Multiple Dirac cones can be engineered by tuning geometry.

Higher-order topological band gaps are realizable in sonic crystals.

Theoretical principles unify Dirac and higher-order topologies.

Abstract

We consider the Dirac cones and higher-order topological phases in quasi-continuous media of classical waves (e.g., photonic and sonic crystals). Using sonic crystals as prototype examples, we revisit some of the known systems in the study of topological acoustics. We show the emergence of various Dirac cones and higher-order topological band gaps in the same motherboard by tuning the geometry of the system. We provide a pedagogical review of the underlying physics and methodology via the bulk-edge-corner correspondence, symmetry-based indicators, Wannier representations, filling anomaly, and fractional corner charges. In particular, the theory of the Dirac cones and the higher-order topology are put in the same framework. These examples and the underlying physics principles can be inspiring and useful in the future study of higher-order topological metamaterials.