Explore the fascinating world of topological phases in quantum matter through this comprehensive lecture by Sumathi Rao at the International Centre for Theoretical Sciences. Delve into the fundamental concepts of topology and its applications in condensed matter physics, starting with the groundbreaking discovery of the integer quantum Hall effect. Examine the bulk-boundary correspondence and edge states, and learn about the recent developments in topological materials, including topological insulators and superconductors. Investigate key models like the Su-Schrieffer-Heeger and Kitaev models, and gain insights into current research frontiers such as Floquet topological phases and the quest for Majorana modes. This in-depth presentation offers a thorough overview of the field, from its historical foundations to cutting-edge advancements, providing valuable knowledge for students, researchers, and professionals interested in quantum physics and materials science.
Overview
Syllabus
Topological Phases of Quantum Matter
arXiv number 1807.10271 - The "High Quality" Topological Materials in the World
Why are topological phases interesting?
What is Topology?
Definition of topological phases
II -First topological phase - 35 years ago integer quantum hall effect
Conventional Hall Effect
Integer quantum Hall effect - 1982
Quantum problem of single electron moving in a perpendicular magnetic field
Topological explanation of the quantisation
III - Edge states and bulk-boundary correspondence
Semi-classical argument
Quantum mechanical - bulk edge correspondence
IV - Topological materials post - 2005
The topological revolution 10-15 years ago - Topological insulators
Topological band theory
Adiabatic continuity and topology
Quantum spin Hall effect
Topological insulators
Time reversal symmetry
Kramer's theorem
What are the consequences?
Real material and experiments in 2D
3D topological insulators
Real materials and experiments in 3D
Topological superconductors
One dimensional topological insulator
Majorana modes
Su-Schrieffer-Heeger model
Edge states in the Su-Schrieffer Heeger model
One dimensional topological superconductor - Kitaev Model
Current frontiers in the field
Floquet topological phases induced by driving
Interplay of interactions and topology
Quest for Majoranas - several ideas
Glimpse of my collaborators
Take-away points
Take-away points cont
Taught by
International Centre for Theoretical Sciences
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