Strategic Objectives
• Master the core principles of Berry phases and geometric phases.
• Understand the mechanics of symmetry-protected topological phases.
• Explore the intersection of quantum mechanics and global geometry.
• Identify real-world applications in quantum computing and spintronics.
The Core Challenge
Traditional material science often fails to explain why certain materials exhibit indestructible edge states and robust conductivity despite internal insulation.
01
The Dawn of Topology
02
Geometric Phase Foundations
03
The Quantum Hall Effect
04
Chern Insulators
05
Time-Reversal Symmetry
06
The Z2 Invariant
07
Bulk-Boundary Correspondence
08
Spin-Orbit Coupling
09
Majorana Bound States
10
Topological Superconductivity
11
Dirac and Weyl Semimetals
12
The Tenfold Way
13
Symmetry-Protected Topological Phases
14
The Kane-Mele Model
15
Experimental ARPES
16
Quantum Spin Hall Effect
17
Topological Quantum Computing
18
Floquet Topological Insulators
19
Magnetic Topological Insulators
20
Topological Crystalline Insulators
21