Higher order topological semimetals and superconductors

This thesis focuses on theoretical investigations and experimental realizations of various topological phases of matter. The first part of thesis extends the notion of higher order topological phases to include the semimetallic and superconducting phases. Upon stacking up the two dimensional higher order topological insulators, we realize four different kinds of higher order topological semimetals with distinct physical observ- ables. The mid-gap hinge states and surface polarizations of these semimetals, which are all consequences of the bulk quadrupole moments, can be extracted from the momentum separations of the bulk or surface nodes in the energy spectrum. The tight-binding model of the higher order topological insulators can be treated as Bogoliubov-de Gennes Hamiltonians of higher order topological superconductors. We propose two kinds of second-order topological superconductivity with different microscopic realizations, and show that it is possible to realize them via proximity effect in a hetero-structure of cuprate and the recently discovered (first order) topological superconductor. We also apply the machinery of topological quantum chemistry to study the spin momentum locking of chiral multifold fermions, and compare to the ab-initio results for a real material. The second part of the thesis includes experimental realizations and applications of the topological phases. Quantum Hall effect has been discovered for more than four decades, and synthetic Hall effect has been an active research in the community of metamaterials. We relate the synthetic Hall effect to a spatiotemporally modulated 1D resonator chain, and demonstrate its strong nonreciprocity. We also demonstrate the trapped state at a dislocation in a weak magnetomechanical topological insulator. Dis- orders, which could be frozen-in during fabrication or appear dynamically in the form of fluctuations, can cause undesirable scattering and localizations in linear waveguides. We show that a temporal modulated 1D magneto-mechanical metamaterial can produce on-demand, robust transport of mechanical energy, which is uniquely resilient to defects occurring in both space and time. These works not only open a path towards exploration of higher-dimensional topological physics using time as a synthetic dimension, but also pave the way for using topologically protected systems for communication, sensing, and broader applications.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Lin, Mao

Contributors dc:contributor

• Hughes, Taylor
• Bradlyn, Barry
• Gadway, Bryce
• Bahl, Gaurav

• Topological insulator
• topological semimetal
• topological superconductor
• higher order topological phase

Statement dc:rights

• © 2022 by Mao Lin. All rights reserved.

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115364

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115364