中文题名: | 基于 SSH 模型的非厄米声学拓扑态调控机制研究 |
姓名: | |
保密级别: | 公开 |
论文语种: | chi |
学科代码: | 070201 |
学科专业: | |
学生类型: | 学士 |
学位: | 理学学士 |
学位年度: | 2023 |
校区: | |
学院: | |
第一导师姓名: | |
第一导师单位: | |
第二导师姓名: | |
提交日期: | 2023-05-24 |
答辩日期: | 2023-05-09 |
外文题名: | Research on control mechanism of non-Hermitian acoustic topological state based on SSH model |
中文关键词: | |
外文关键词: | SSH model ; non-Hermiticity ; phononic crystal ; acoustic topological states |
中文摘要: |
在凝聚态物理中,拓扑绝缘体的发现颠覆了人们以往对传统绝缘体的认知,也激发了人们对经典波体系的拓扑现象的研究。声波、光波等经典波体系是一个观察拓扑现象的绝佳平台,声学拓扑相的研究也逐渐成为近年的研究热点。具有拓扑保护的边界态能够抑制背向散射,对于系统缺陷具有较强的鲁棒性,使其在声通信、噪声控制和隔声领域有较大的应用。 在量子力学中,除了对传统的厄米系统的研究,人们对非厄米体系的研究兴趣也逐渐增加。非厄米系统时刻与外界环境有能量交换,具有较为复杂的能谱,通常需要用非厄米算符来描述。进一步研究者发现非厄米算符的本征值在满足PT对称性下可以为实数,而当PT对称性破缺时本征值变为复数。将非厄米系统引入经典波体系,可以实现传统厄米系统无法实现的奇异现象。同时,声子晶体由于制备简单且对声波具有可操控性,为研究非厄米性提供一个理想平台。人们在声子晶体中引入非厄米调制,实现了许多声波操纵的新奇现象,为现代声学的研究注入新的能量。 在这些声学拓扑态的研究中,Su-Schrieffer-Heeger (SSH)模型作为一种最简单的二能带物理系统,为非厄米系统下声学拓扑态的研究提供了一个很好的平台。SSH模型描述了无自旋费米子在具有交错振幅的一维晶格上的跳跃,其拓扑零模的边缘态具有丰富的拓扑特征。首先我们建立一维周期性结构的声子晶体模型,对声学拓扑态的性质进行探究,然后通过在经典的SSH模型引入非厄米调制,我们研究了非厄米性对声学拓扑态的调控机制,并观测到了一些奇特的声波传输特性。 |
外文摘要: |
In condensed matter physics, the discovery of topological insulators overturns people's previous cognition of traditional insulators and stimulates people's research on the topological phenomena of classical wave systems. Classical wave system such as sound wave and optical wave is an excellent platform for observing topological phenomena, and the study of acoustic topological phase has gradually become a research hotspot in recent years. Topological edge states can suppress backscattering and have strong robustness to system defects, making them widely applied in the fields of acoustic communication, noise control and sound insulation. In quantum mechanics, in addition to the study of traditional Hermitian systems, people are increasingly interested in non-Hermitian systems. Non-Hermitian systems usually have relatively complex energy spectra, so it can be used to describe open systems, that is, systems have energy exchange with the external environment at all times. Further, it is found that the eigenvalues of non-Hermitian operators can be real if PT symmetry is satisfied, and the eigenvalues become complex when PT symmetry is broken. Introducing the non-Hermitian system into the classical wave system can realize the interesting phenomenon that the traditional Hermitian system cannot achieve. Phononic crystals provide an ideal platform for the study of non-Hermitian properties due to their simple preparation and control-ability to sound waves. Many novel phenomena of acoustic manipulation have been realized by introducing non-Hermitic modulation into phononic crystals, which has inspired new energy into the study of modern acoustics. In the study of these acoustic topological states, Su-Schrieffer-Heeger(SSH) model, as one of the simplest two-band physical systems, provides a good platform for the study of acoustic topological states in non-Hermitian systems. The SSH model describes electrons hopping on a one-dimensional lattice with staggered hopping amplitudes, and the topological zero mode edge states have rich topological features. Firstly, we establish a phononic crystal model with one-dimensional periodic structure to explore the properties of acoustic topological states. Then, by introducing non-Hermitian modulation into the classical SSH model, we study the regulation mechanism of non-Hermitian properties on acoustic topological states, and observe some novel acoustic transmission characteristics. |
参考文献总数: | 42 |
插图总数: | 20 |
插表总数: | 0 |
馆藏号: | 本070201/23008 |
开放日期: | 2024-05-23 |