Position-space and spin signatures of higher-order topological insulators

Topology of non-interacting electrons in crystalline solids can be formulated in terms of suitable momentum-space integrals. Non-trivial topology can lead to observable signatures, which could be probed in the position space as well as through the response of certain degrees of freedom, such as the electric charge and electron spin. This thesis reports several works studying position-space and spin signatures of topological phases, in particular higher-order topological insulators (HOTIs). In the first part of this thesis, we study density wave systems whose microscopic Hamiltonians exhibit position-space modulations. We show how to use density wave systems and their sliding phason degrees of freedom as the proxy to study (higher-order) topological states in dimensions higher than the density wave systems themselves. The corresponding position-space feature is the existence of boundary-localized states as well as the layered structure of topological wave functions when the phason slides. In the second part of this thesis, we study systems with spin degrees of freedom. We introduce the notion of spin-resolved topology through gauge-invariant methods as a probe to systematically study the topology of spin-up and spin-down electrons in the ground state. We extend the Wilson loop and layer construction methods in terms of the spin-resolved topology. We employ such extensions to derive various spin signatures of systems with non-trivial topology. We also extend the formalism of position-space Chern number through the spin-resolved topology. This allows us to demonstrate anomalous surface properties of certain HOTIs, for which we identify the materials candidate. Spin-resolved topology not only provides a refinement of the electronic band topology but also allows us to study the position-space and spin signatures of topological states.

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

2024

Author dc:creator

• Lin, Kuan-Sen

Contributors dc:contributor

• Bradlyn, Barry
• Hughes, Taylor L.
• Madhavan, Vidya
• Covey, Jacob P.

• Topological
• Phases Of Matter
• Density Waves
• Topological Insulators
• Topological Crystalline
• Insulators
• Higher-order
• Topological Materials

Statement dc:rights

• Copyright 2024 Kuan-Sen Lin

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127135

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127135