Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Victor Gurarie

Second Advisor

Rahul Nandkishore

Third Advisor

Michael Hermele

Fourth Advisor

Leo Radzihovsky

Fifth Advisor

Markus Pflaum

Abstract

Topological quantum phases of matter are often characterized by the presence of fractionalized quasiparticles, which exhibit non-trivial braiding statistics or carry fractional quantum numbers, or of protected gapless surface states. In this thesis, we study topological phases in two and three spatial dimensions, from the perspective of searching for new exotic quantum phases and of characterizing their experimental signatures.

We first study topological defects in fermionic paired superfluids and discover that in the presence of a multiply quantized vortex, such a state hosts unpaired fermions in the BCS regime. We predict that these unpaired fermions will result in an experimentally measurable deviation of the system's angular momentum from its value in the BEC regime. Focusing on two-dimensions, we then study superconductors coupled to dynamically fluctuating electromagnetism, and establish a universal framework for studying the low-energy physics of such systems. We derive topological field theories describing all spin-singlet superconductors which naturally capture the interplay of symmetry and topology in these gapped states.

The remainder of this thesis is focused on a novel class of long-range entangled states of matter, known as “fracton” phases, in both two- and three-dimensions. These phases exhibit an intriguing phenomenology, most surprising of which is the presence of excitations which are immobile in isolation. Studying the non-equilibrium dynamics of gapped fracton phases, we discover that they naturally exhibit glassy quantum dynamics in the absence of quenched disorder, and hence may have potential technological applications as robust quantum memories. Finally, we conclude with a description of fracton phases as higher-rank tensor gauge theories and discuss the emergent phases of matter in which a finite density of fractons or their bound states may exist.

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