Higher-rank gauge theories in condensed matter physics
Dubinkin, Oleg
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https://hdl.handle.net/2142/117639
Description
Title
Higher-rank gauge theories in condensed matter physics
Author(s)
Dubinkin, Oleg
Issue Date
2022-10-31
Director of Research (if dissertation) or Advisor (if thesis)
This thesis summarizes my efforts to bridging the gap between two recently proposed classes of topological matter: higher-order topological insulators (HOTI) and fracton phases of matter. Getting a clear under- standing of these systems will answer fundamental questions about the effects of symmetry and topology in quantum materials and open doors to novel devices. In particular, fracton states have the potential to serve as building blocks for quantum hard drives and logic elements, and HOTIs can exhibit robust electronic modes and electromagnetic responses. These classes of quantum phases are unified by the existence of additional conservation laws, e.g., conservation of the electric dipole moment. In HOTI phases dipole conservation is typically a ground-state property that allows the system to have a well-defined electric quadrupole moment which generates protected electronic states and/or fractional charge localized at the corners of a sample. In fracton phases, dipole conservation is a microscopic conservation law that greatly constrains the motion of individual charges around the system. In both cases, the added conservation laws are often tied to symmetries of the underlying lattices, which in turn places crystalline symmetries at the forefront of my research.
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