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

School of Physical Science and Technology & Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University - Suzhou 215006, China

^(a) jianhuajiang@suda.edu.cn (corresponding author)

Received: 26 October 2021
Accepted: 24 February 2022

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 framework 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.