Topology and the Electromagnetic Responses of Quantum Materials

Explore the fascinating world of quantum materials and their electromagnetic responses in this 30-minute conference talk by Joel E. Moore at the International Centre for Theoretical Sciences. Delve into the concepts of topology, Berry gauge fields, and topological invariants in solids. Examine the intricacies of Berry phase and its application to solids, with a focus on topological insulators in 3D. Investigate the quantization of electromagnetic responses in insulators and the unique properties of graphene. Discover the anomalous Hall effect and other mysterious phenomena in metals, including 3D Dirac and Weyl metals. Learn about current research questions and experimental evidence for nonlinear effects in Weyl semimetals. Explore the quantized circular photogalvanic effect in mirror-free 3D-Weyl semimetals and its implications for quantum materials research. Gain insights into the cutting-edge developments in condensed matter and statistical physics through this comprehensive overview of topology and electromagnetic responses in quantum materials.

Start
Topology and the electromagnetic responses of quantum materials
General themes
Outline
Types of order
Overview: Berry gauge fields in solids
Topological invariants
Berry phase
Berry phase in solids
Topological insulator in 3D
What is quantized in a 3D TI? Electrodynamics in insulators...
Axion E&M
Graphene QHE
Topological response
What about metals?
Anomalous Hall effect 100+ years
Two other "mystery" effects in metals:
3D Dirac and Weyl metals
Active questions:
Outline of CME and GME
So linear response is "geometric" in metals, but not quantized
Experimental evidence that nonlinear effects are interesting in Weyls
A quantized effect in Weyl semimetals
Quantized CPGE
What is the "quantum"?
The circular photogalvanic effect in mirror-free 3D-Weyl semimetals is quantized
Conclusions
Q&A