ECE 69500 - Topological Electrodynamics

Course Details

Lecture Hours: 3 Credits: 3

Areas of Specialization:

  • Fields and Optics

Counts as:

Normally Offered:

Fall - even years


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):


Recommended Text(s):

  1. 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