Key Information
About the content
This course introduces the Schrödinger equation, using the tight-binding method to discuss the concept of bandstructure and E(k) relations, followed by an introduction to the NEGF method with simple illustrative examples. Concept of spinors is introduced along with the application of the NEGF method to spintronic devices.
No prior background in quantum mechanics or statistical mechanics is assumed.
This course is a part of a Purdue initiative that aims to complement the expertise that students develop with the breadth at the edges needed to work effectively in today's multidisciplinary environment. These serious short courses require few prerequisites and provide a general framework that can be filled in with self-study when needed.
Students taking this course will be required to complete three (3) proctored exams using the edX online Proctortrack software.
Introduction to Quantum Transport is one course in a growing suite of unique, 1-credit-hour short courses being developed in an edX/Purdue University collaboration. Students may elect to pursue a verified certificate for this specific course alone or as one of the six courses needed for the edX/Purdue MicroMasters program in Nano-Science and Technology. For further information and other courses offered and planned, please see the Nano-Science and Technology page. Courses like this can also apply toward a Purdue University MSECE degree for students accepted into the full master’s program.
- The Schrödinger equation
- How the tight-binding model works
- The concept of bandstructure and E(k) relations
- Self-energy
- Broadening
- NEGF equations
- Dephasing
Prerequisite
Undergraduate degree in engineering or the physical sciences, specifically differential equations and linear algebra.
Syllabus
Week 1: Schrödinger Equation
1.1 Introduction
1.2 Wave Equation
1.3 Differential to Matrix Equation
1.4 Dispersion Relation
1.5 Counting States
Week 2: Schrödinger Equation (continued)
1.6 Beyond 1D
1.7 Lattice with a Basis
1.8 Graphene
1.9 Reciprocal Lattice/Valleys
1.10 Summing Up
Week 3: Contact-ing Schrödinger & Examples
2.1 Introduction
2.2 Semiclassical Model
2.3 Quantum Model
2.4 NEGF Equations
*2.5 Bonus Lecture, NOT covered on exams
2.6 Scattering Theory
Week 4: Contact-ing Schrödinger & Examples (continued)
2.7 Transmission
2.8 Resonant Tunneling
2.9 Dephasing
2.10 Summing Up
3.1 Bonus Lecture, NOT covered on exams
3.2 Quantum Point Contact
__ 3.3 - 3.10 Bonus Lectures, NOT covered on exams
Week 5: Spin Transport
4.1 Introduction
4.2 Magnetic Contacts
4.3 Rotating Contacts
4.4 Vectors and Spinors
4.5 - 4.6 Bonus Lectures NOT covered on exams
4.7 Spin Density/Current
__ 4.8-4.10 Bonus Lectures NOT covered on exams
Text: S. Datta, “Lessons from Nanoelectronics”, Part B: Quantum Transport, World Scientific, Second Edition 2017
The manuscript will be available for download at the course's website.
Instructors
Supriyo Datta
Thomas Duncan Distinguished Professor of Electrical and Computer Engineering, NAE member
Purdue University
Shuvro Chowdhury
PhD Student
Purdue University
Platform
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