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Enriching Majorana Zero Modes

Citation

Chew, Aaron (2020) Enriching Majorana Zero Modes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/91q9-9606. https://resolver.caltech.edu/CaltechTHESIS:05142020-114820618

Abstract

My various projects in graduate school have centered around a common theme: harnessing relatively well-understood phases of matter and combining them to create exotic physics. They also involve Majoranas, or more accurately, defects that bind Majorana zero modes and are the centerpiece for topological quantum computation. We exploit and enrich this Majorana zero mode by employing topological superconductors, time crystals, and quantum dots and combining them together. Our first project involved joining Majorana nanowires and quantum dots to simulate the SYK model, a zero-dimensional strongly interacting phase with connections to black holes and holography. We follow by explaining how to combine spontaneous symmetry-breaking with topological superconductivity to recover parafermion physics in one dimension. We explain an exact mapping that relates fermions to parafermions, illustrating a deep connection between different one-dimensional phases of matter. We finally show that enhancing the topological superconductor with a time crystal, a phase of matter that spontaneously breaks time-translation symmetry, creates an anomalous zero mode that displays 4Tperiodicity in the Floquet drive. By combining these different phases in judicious ways we achieve exotic physics unattainable by the constituent parts. Our work thus illustrates profitable directions for harnessing Majorana zero modes to study the physics of exotic matter.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Majorana zero modes; topological phases of matter; topological superconductivity
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Alicea, Jason F.
Thesis Committee:
  • Chen, Xie (chair)
  • Alicea, Jason F.
  • Motrunich, Olexei I.
  • Nadj-Perge, Stevan
Defense Date:11 May 2020
Funders:
Funding AgencyGrant Number
Dominic Orr FellowshipUNSPECIFIED
Yunni and Maxine Pao FellowshipUNSPECIFIED
NSFDMR-1341822
NSFDMR-1723367
Army Research Office (ARO)W911NF-17-1-0323
Gordon and Betty Moore FoundationGBMF1250
Institute of Quantum Information and MatterUNSPECIFIED
Walter Burke Institute for Theoretical PhysicsUNSPECIFIED
Record Number:CaltechTHESIS:05142020-114820618
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05142020-114820618
DOI:10.7907/91q9-9606
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.96.121119DOIArticle adapted for Chapter 2.
https://doi.org/10.1103/PhysRevB.98.085143DOIArticle adapted for Chapter 3.
https://doi.org/10.1103/PhysRevLett.124.096802DOIArticle adapted for Chapter 4.
ORCID:
AuthorORCID
Chew, Aaron0000-0003-0448-6215
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13705
Collection:CaltechTHESIS
Deposited By: Aaron Chew
Deposited On:01 Jun 2020 21:43
Last Modified:18 Dec 2020 01:36

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