Explore the intricacies of higher-order topological crystalline insulators (HOTIs) in this comprehensive lecture. Delve into the bulk signatures of helical TCIs and their relationship to sample-independent experimental observables. Discover the three distinct spin-resolved phases of helical HOTIs: 3D quantum spin Hall insulators, "spin-Weyl" semimetal states, and T-doubled axion insulator (T-DAXI) states. Examine the quantitatively robust responses of these phases to large deformations of the bulk spin-orbital texture. Investigate experimental signatures for each spin-stable regime, including surface Fermi arcs in spin-Weyl semimetals under strong Zeeman fields and half-quantized 2D TI states on gapped surfaces of T-DAXIs. Learn about flux insertion, position-space partial Chern markers, and newly introduced nested spin-resolved Wilson loops and spin-resolved layer constructions used to fully characterize the bulk topological properties of inversion- and T-protected helical HOTIs.
Spin-Resolved Topology and Partial Axion Angles in Higher-Order Topological Crystalline Insulators
PCS Institute for Basic Science via YouTube
Overview
Syllabus
Intro
Why Do We Care About Topological States?
The Response Theory of 3D Tls is Axion Electrodynamics
Higher-Order Topology is a Useful Theory Framework
Higher-Order Topology is Experimentally Ambiguous
Signature of 3D Chiral HOTIS: Axion Electrodynamics
Test: Dislocations and Magnetic Flux Insertion
Test Case: Chiral HOTI (Axion Insulator)
Theory Interpretation of Flux Insertion
Position-Space Calculations Reveal a New Anomaly
Finer Classification of Insulators: Spin-Resolved Topology
Taught by
PCS Institute for Basic Science
