This lecture focuses on basic understanding of the topological properties of materials and discusses the applications of information devices and topological quantum computers based on topological materials. To achieve this, we first study basic quantum mechanics and methods for calculating the band structure of materials, and discuss the topological properties of wave functions. Next, we study about the topological properties of two-dimensional semiconductor materials and graphene, and understand the theoretical descriptions of topological systems such as topological insulators, topological superconductors, and the quantum Hall effect. Based on this knowledge, we further explore the recent device applications through reviewing information devices based on the topological quantum materials, and the implementation of topological quantum computers.

Basic knowledge of quantum mechanics, Basic knowledge of Condensed matter physics or physical electronics
: Quantum Mechanics, Physics of Materials, Physical Electronics, Quantum Chemistry, or any equivalents.

Attendance, Homework, Final

Week 1~3 : Basic quantum mechanics in a solid
- Introduction to Quantum Mechanics, Schrodinger Equation
- Aharanov-Bohm Effect, Adiabatic Theorem
- Berry Phase, Berry Curvature, Topological Invariants
- Schrodinger Equation in a solid
- Band Theory and Tight binding method – Graphene, 2D Semiconductors
Week 4~7 : Topological Systems I
- 1D Topological systems : SSH Model
- 2D Topological system I : Quantum Hall Effect, Adiabatic Charge Pumping
- Berry phase description of Electric Polarization, Ferroelectricity
- 2D Topological system II : Quantum Anomalous Hall Effect (Haldane model, QWZ model), Bulk-boundary correspondence
- 2D Topological system III : Quantum Spin Hall Insulator (Kane-Mele Model, BHZ model), Z2 invariants
Week 8 : Mid-term Exam
Week 9 : Topological Systems II
- 3D Topological Insulator
- Topological Properties of 2D Semiconductors
- Fractional Quantum Hall system
- Topological Superconductors
Week 10~13: Topological Quantum Computation
- Anyon models and braiding anyons
- Quantum Gates – Braiding Anyons
- Quantum Measurement – Fusing Anyons
- Majorana zero mode in a superconducting nanowire
- Manipulating and Reading out Majorana qubits
Week 14~15: Topological Devices Applications
- Topological Ferroelectric/Ferromagnetic Devices
- Topological field-effect transistors, Topological PN Junctions
- Topological Magnetic Devices (SOT-based topological device, Magneto-electric effect-based topological device
Week 16 : Final Exam

Offline class 100%