ECE 69500 - Topological Electrodynamics
Course Details
Lecture Hours: 3 Credits: 3
Areas of Specialization:
- Fields and Optics
Counts as:
Normally Offered:
Fall - even years
Campus/Online:
On-campus only
Requisites by Topic:
Undergraduate coursework on electromagnetics, electronic devices, and differential equations.
Catalog Description:
Exciting research trends in the fields of topological electronic materials have motivated a unique set of closely related phenomena in photonics and phononics. This course will introduce graduate students to foundational ideas such as Pancharatnam-Berry Phase, Chern number, topological surface states, spin-momentum locking and quantum spin hall effect. These phenomena will be covered with themes cross-cutting the fields of electronics, photonics and phononics. Throughout the course, quantum and thermal engineering applications will be stressed. These include quantum communications, quantum gates, quantum memories, robust on-chip photonic-routing, spin-sensing, single photon detectors, ultralow threshold lasing, etc.
Required Text(s):
None.
Recommended Text(s):
- Geometric Phases in Classical and Quantum Mechanics , Dariusz Chruscinski, Andrzej Jamiolkowski , Springer Science & Business Media , 2012 , ISBN No. 9780817681760
Lecture Outline:
| 1 | Topic(s) |
|---|---|
| 1 | Parity and time-reversal symmetry for fermions and bosons |
| 2 | Introduction to spin and orbital angular momentum for fermions and bosons |
| 3 | Topological quantization vs. second quantization |
| 4 | Graphene as a model system for topological phase, introduction to geometric phase and Chern number |
| 5 | Dirac equation and topological edge states |
| 6 | Quantum and topological phase transitions, quantum magnets |
| 7 | Integer quantum hall effect, quantum spin hall effect, topological Insulators in 2D and 3D, Weyl semi-metals |
| 8 | Selected experiments on topological phases of matter |