Document Type


Date of Award


Degree Name

Doctor of Philosophy in Materials Science and Engineering - (Ph.D.)


Committee for the Interdisciplinary Program in Materials Science and Engineering

First Advisor

Camelia Prodan

Second Advisor

John Francis Federici

Third Advisor

Ken Keunhyuk Ahn

Fourth Advisor

Michael Siegel

Fifth Advisor

Smitha Vishveshwara


Topological acoustics is a recent and intense area of research. It merges the knowledge of mathematical topology, condensed matter physics, and acoustics. At the same time, it has been pointed out that quasiperiodicity can greatly enhance the periodic table of topological systems. Because quasiperiodic patterns have an intrinsic global degree of freedom, which exists in the topological space called the hull of a pattern, where the shape traced in this topological space is called the phason. The hull augments the physical space, which opens a door to the physics of the integer quantum Hall effect (IQHE) in arbitrary dimensions. In this dissertation, acoustic metamaterials that exhibit two-dimensional (2D) and four-dimensional (4D) IQHE physics are demonstrated by laboratory implementation based on these ideas. In the second chapter, the acoustic waveguide generated by a simple quasiperiodic patterning exhibits topological edge modes and interface modes without any additional fine-tuning. In the third chapter, acoustic metamaterials generated by incommensurate bilayers present dynamic energy transfer in adiabatic cycles across the crystal via pumping of topological edge modes without any external intervention or assistance. In the fourth chapter, a re-configurable 2D quasiperiodic acoustic crystal with a phason living on a 2-torus displays 4D quantum Hall physics. The topological boundary spectrum assembles in a Weyl singularity when mapped as the function of the quasi-momenta. Topological wave steering enabled by the Weyl physics of the three-dimensional (3D) boundaries is also demonstrated experimentally. All acoustic systems mentioned previously are characterized experimentally by standard acoustic measurements, and via a finite element analysis utilizing COMSOL Multiphysics. The experimental measurements and simulations reproduce the theoretical predictions with high fidelity.



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