Study on several novel topological phases in sonic wave systems

Abstract

A phase transition occurs when the order parameter changes, such as in the case of ice melting into water or paramagnets changing into ferromagnets. In 2016, David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz won the Nobel Prize in Physics for their pioneering work on topological phase transitions. Unlike conventional phases, which are characterized by order parameters, topological phases are described by topological invariants. Due to the novelty of topological phases, extensive research has been conducted on the topological phases of matter, ranging from condensed matter physics to photonics, phononics, and circuits. Because experiments in electronic systems are extremely challenging, many topological matter models have been demonstrated in classical wave systems, such as photonics and acoustics. The discovery of new topological phases opens up possibilities for new theories and novel applications. In this thesis, I study several novel topological phases in acoustic systems, including experimental demonstrations of three-dimensional Landau levels, π/2 modes in the Floquet system, and disorder-induced skin effects.

In Chapter 1, I briefly review the history of topological phases in condensed matter physics and classical wave systems. I introduce the basic knowledge and concepts of topological phases, along with some preliminary information about the quantum Hall effect, Floquet systems, and disordered systems, which I will study in detail in the following chapters.

In Chapter 2, I study the quantum Hall effect and Landau quantization. I extend the Landau quantization to quasiparticles in the nodal ring system, observing three-dimensional flat Landau levels and drumhead states in the acoustic structure.

In Chapter 3, I study topological properties in the Floquet system. Using the slowly varying amplitude approximation and the concept of synthetic dimension, we observe π/2 modes in addition to the conventional zero and π edge modes in the experiment.

In Chapter 4, I study topological phases in disordered systems. Disorder can induce metal-insulator transitions and topological Anderson localization. Here, I extend the study of disorder to non-Hermitian systems. With increasing disorder strength, the system exhibits multiple phase transitions, including delocalization-localization-delocalization-localization transitions.