| Author: | Fan, Haiyan |
| Title: | Non-Hermitian topological phases in elastic and acoustic lattices |
| Advisors: | Su, Zhongqing (ME) Zhu, Jie (ME) |
| Degree: | Ph.D. |
| Year: | 2023 |
| Award: | PolyU PhD Thesis Award - Merit Award (2024) |
| Subject: | Topology Metamaterials Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Mechanical Engineering |
| Pages: | xxxiv, 157 pages : color illustrations |
| Language: | English |
| Abstract: | Classical wave systems have been fertile grounds where topological physics are investigated, enabling the discoveries of numerous intriguing phenomena such as backscattering-free chiral edge states associated with the quantum Hall–like effect and localized edge (corner) modes due to the quantized bulk dipole (quadrupole) moments. Much effort in this field has hitherto dedicated to the Hermitian Hamiltonians characterized by real-valued eigenfrequencies and orthogonal eigenvectors, while the intrinsically lossy nature of classical wave systems has inspired explorations towards their non-Hermitian counterparts for more realistic experimental investigations and practical applications. In this thesis, a series of non-Hermitian topological phenomena are explored in elastic and acoustic lattices, aiming at offering new opportunities to explore topological physics and their potential applications in acoustic and elastic wave manipulation. This thesis starts with one-dimensional (1D) perturbative elastic metamaterials based on the Su–Schrieffer–Heeger (SSH) model to investigate the Hermitian topological edge states and their non-Hermitian counterparts. The designed metamaterials are tight-binding chains consisting of square plates (corresponding to mass points) connected by thin beams (corresponding to rigid bonds). For the hypothetically Hermitian case, alternating coupling strengths contribute to dimerization which gives rise to topologically non-trivial and trivial band gaps as well as the associated topological edge states. For the non-Hermitian case, uneven absorptive damping treatments applied to the double-sized unit cell modulate the system in a similar way as the uneven damping treatments are capable of creating topological edge states even under identical coupling strength. In the next chapter, it is shown that the topological edge states can be shifted to coexist with a bulk band, rather than emerging in a band gap as commonly seen, forming the so-called topological bound states in the continuum (BICs). These embedded topological states are observed in a 1D trimerized elastic lattice, which are produced solely by non-Hermiticity realized using constrained damping layers attached to particular sites in the finite-sized chain assembly. The results indicate that appropriately tailored non-Hermitian modulation can induce topological edge states that appear in the bulk spectrum, not necessarily requiring the construction of band gaps. This thesis further extends the 1D topological phenomena to a two-dimensional (2D) space, which could control not only the first-order topological edge states but also the second-order topological corner states. Different from the conventional wisdom that a topological state is usually altered with varied topological phase, this chapter shows an exception in non-Hermitian acoustic crystals. In an acoustic quadrupole topological insulator (QTI), its topological corner, edge and bulk states can be arbitrarily engineered at any desired positions with its topological phase maintained. These non-Hermiticity-controlled topological states bestow a bulk structure with unique features and versatilities not available in Hermitian scenarios. The above studies only concern topological phenomena in either fluids or solids alone, with fluid-solid interactions neglected. The following chapter attempts to answer the question on how intricate fluid-solid interactions in “mixtures” can breed novel topological physics. With a simple three-dimensional (3D) phononic crystal immersed in water, this chapter shows that the unique interplay between fluids and solids can be utilized to realize type-II nodal rings, elusive in phononics. Strongly tilted drumhead surface states, the hallmark phenomena, are also experimentally demonstrated. In summary, starting from 1D elastic lattices to 2D acoustic lattices, and finally to a 3D phononic crystal with fluid-solid interaction coming into play, multiple new breeds of topological phenomena are demonstrated both in theory and experiment. These results extend the topological physics beyond the conventional Hermiticity assumption and offer reconfigurable and versatile approaches to manipulating topological phenomena. Besides, these phononic approaches open a door to explore topological physics in classical systems, which is easy to implement and can be used for designing high-performance devices. |
| Rights: | All rights reserved |
| Access: | open access |
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