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 Title: Higher-order crystalline topology in resonator circuits Author(s): Peterson, Christopher W Director of Research: Bahl, Gaurav Doctoral Committee Chair(s): Bahl, Gaurav Doctoral Committee Member(s): Bernhard, Jennifer T; Fang, Kejie; Hughes, Taylor L Department / Program: Electrical & Computer Eng Discipline: Electrical & Computer Engr Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): topological insulator higher-order topological insulator crystalline topology higher-order crystalline topology microwave resonator microstrip resonator resonator circuit fractional charge quadrupole topological metamaterials Abstract: Symmetries play a vital role in physics, forming the core of the most fundamental theories about our universe. When symmetries are enforced in materials having an energy gap, certain properties of the material can become quantized to specific values that remain constant even if the material is deformed. These fixed properties, known as topological invariants, are robust to any deformation of the material as long as it preserves both the energy gap and relevant symmetries. The discovery of materials hosting such invariants, known as topological insulators, was awarded the 2016 Nobel Prize in Physics. At the boundary of a topological insulator where topological invariants change in space, the energy gap closes, creating robust states that cannot be removed from the boundary. Due to this property, which promises to enable more efficient and robust devices for applications ranging from quantum computing to fiber-optic communications, topological insulators are currently the topic of considerable research. Because all fundamental particles (electrons, photons, etc.) share the same wavelike properties, the concepts of topological invariants and topological insulators can be extended beyond real materials to so-called metamaterials, where the fundamental atom" is no longer composed of protons and neutrons, but of some larger engineered material that forms an effective atom for light or sound. These topological metamaterials not only serve as devices having unique properties such as robust nonreciprocal transport or self-healing, but also enable research into designed topological insulators that may not occur naturally. One area where topological metamaterials have attracted research efforts is in the study of higher-order topological insulators, a recently discovered class of topological insulators where robust states appear not at boundaries, but at boundaries of boundaries. This dissertation presents several experimental studies of higher-order topological insulators protected by crystalline symmetries, which were all physically realized in microwave-frequency metamaterial circuits. The first is an implementation of a quadrupole topological insulator, the first higher-order topological insulator to be discovered. Following this initial study, many experiments have demonstrated higher-order topological metamaterials. However, in many cases the identification of these systems relies upon localized, in-gap corner modes, which are not robust to local perturbations and thus not reliable topological indicators. The other two experimental studies presented in this dissertation attempt to solve this problem by introducing a new method for identification - measurement of fractional charge (or fractional mode density). Both focus on rotationally symmetric systems, the first demonstrating that fractional charge manifesting at boundaries can indicate non-trivial higher-order topology, and the second demonstrating that fractional charge trapped at defects can be used for the same purpose. The results presented in this dissertation represent the birth of research into higher-order topological insulators as well as the methodology improvements necessary for the field to develop. Furthermore, this work fulfills the promise made more than 40 years ago by Jackiw and Rebbi (and later by Su, Schrieffer, and Heeger) that electronic band topology can generate charge fractionalization. Issue Date: 2020-06-24 Type: Thesis URI: http://hdl.handle.net/2142/108665 Rights Information: Copyright 2020 Christopher Peterson Date Available in IDEALS: 2020-10-07 Date Deposited: 2020-08
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