Document Type


Date of Award


Degree Name

Doctor of Philosophy in Applied Physics - (Ph.D.)



First Advisor

Camelia Prodan

Second Advisor

Ken Keunhyuk Ahn

Third Advisor

Benjamin P. Thomas

Fourth Advisor

S. Basuray

Fifth Advisor

Edward Michael Bonder


The topological concepts of electronic states have been extended to phononic systems, leading to the prediction of topological phonons in a variety of materials. These phonons play a crucial role in determining material properties such as thermal conductivity, thermoelectricity, superconductivity, and specific heat. The objective of this dissertation is to investigate the role of topological phonons at different length scales.

Firstly, the acoustic resonator properties of tubulin proteins, which form microtubules, will be explored The microtubule has been proposed as an analog of a topological phononic insulator due to its unique properties. One key characteristic of topological materials is the existence of edge modes within the energy gap. These edge modes allow energy to be transferred at specific frequencies along the edges of the material, while the bulk remains unaffected. In the case of microtubules, its ability to store vibrational energy at its edges and the sensitivity to changes in local bulk structure align with the properties of topological insulators. Furthermore, the appearance of edge modes in topological phononic insulators is determined by the local interactions of the bulk material. Even small changes in the local structure can shift the resonant frequency of the edge mode or completely extinguish it. Similarly, the ability of microtubules to shorten or overcome energy barriers is greatly affected by changes in their local bulk structure. This suggests a parallel between the impact of local bulk structure on both topological insulators and microtubules. This similarity has led to the proposal that microtubules could serve as an analog of topological phononic insulators, providing insights into their dynamics and potential applications in fields such as chemotherapy drug development and nanoscale materials.

Secondly, the application of topological phonons in the realm of acoustic metamaterials will be examined. Acoustic waves have recently become a versatile platform for exploring and studying various topological phases, showcasing their universality and diverse manifestations. The unique properties of topological insulators and their surface states heavily rely on the dimension and symmetries of the material, making it possible to classify them using a periodic table of topological insulators. However, certain combinations of dimensions and symmetries can impede the achievement of topological insulation. It is of utmost importance to preserve symmetries in order to maintain the desired topological properties, which necessitates careful consideration of coupling methods. In the context of discrete acoustic resonant models, efficiently coupling resonators while simultaneously preserving symmetry poses a challenging question. In this part, a clever experimental approach is proposed and discussed to couple acoustic crystals. This modular platform not only supports the existence of topologically protected edge and interface states but also offers a convenient setup that can be easily assembled and disassembled. Furthermore, inspired by recent theoretical advancements that draw on techniques from the field of C*-algebras for identifying topological metals, the present study provides direct observations of topological phenomena in gapless acoustic crystals. Through these observations, a general experimental technique is realized and developed to demonstrate the topology of such systems. By employing the method of coupling acoustic crystals, the investigation unveils robust boundary-localized states in a topological acoustic metal and presents a reinterpretation of a composite operator as a new Hamiltonian. This reinterpretation enables the direct observation of a topological spectral flow and facilitates the measurement of topological invariants.

Through these investigations, the aim of this dissertation is to deepen our understanding of the significance and potential applications of topological phonons in diverse systems.



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