This course introduces the non-equilibrium Green’s function (NEGF) method widely used to describe quantum effects in nanoscale devices, along with its applications to spintronic devices. 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.
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No prior background in quantum mechanics or statistical mechanics is assumed.
This course is part of the Nanoscience and Technology MicroMasters.
What you'll learn
- The Schrödinger equation
- How the tight-binding model works
- The concept of bandstructure and E(k) relations
- Self-energy
- Broadening
- NEGF equations
- Dephasing
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 in the course.
