Several topological phases and their realization in classical wave systems

• Main Author: Wang, Zihao
• Other Authors: Zhang Baile
• Format: Thesis-Doctor of Philosophy
• Language: English
• Published: Nanyang Technological University 2024
• Subjects: Physics
• Online Access: https://hdl.handle.net/10356/173589
• Institution: Nanyang Technological University

The concept of topological phases has significantly reshaped our understanding of condensed matter physics. In recent years, there has been a growing realization that these exotic phases can also manifest in classical wave systems, offering a novel platform for exploring topological phases. This thesis delves into the exploration and characterization of kinds of novel topological phases in classical wave systems including photonic and acoustic crystals. To begin, we offer a thorough historical examination of the topological phases of matter, delving into the evolution of these phases in classical wave systems. Subsequently, our discussion shifts to higher-order topological phases, semimetal phases, and phases augmented by gauge fields. By combining the concepts of topological semimetal phase and higher-order topological phase, a higher-order Dirac semimetal that can support a hinge state in a three dimensional structure is demonstrated in a photonic crystal. The hinge state appears when the system is in the topological nontrivial phase, as evidenced by the linear Dirac point splits, and regenerates when kz changes. However, in addition to linear dispersion, various types of degeneracy points can develop in topological insulators. In the following work, a quadratic surface state supported by a topological insulator without spin-orbit coupling is demonstrated in a photonic crystal. This state can spread on the surface between the sample and the air without any cladding, indicating a promising use. Then, two works in acoustic crystals reveal topologically protected braiding, such as Möbius loop and three staggered braidings in the insulating gap. When a Z2 gauge is applied to the lattice, the original symmetry will be projectively enriched and presented giving out such novel states at the edge. Finally, a summary and perspective for future directions and ideas are presented. These works not only illustrate multiple unique topological phases in classical wave systems, but also pave the path for the use of topologically protected systems in communication, sensing, and other applications.