Greens function approach to transport

Erich Mueller

Jan 24-Feb 16

Where does resistivity come from? How can one calculate the resistivity of an actual device? In this 4 week module we will explore these questions, and learn an important tool for studying many-body problems: Greens functions.

Students should have completed an introductory solid state physics class, such as PHYS 7635, so that they are familliar with band-structure and the Drude theory of conductivity. No prior exposure to many-body Greens functions is assumed, but students should be familliar with second quantization. Students who believe they might need some extra preparation should feel free to contact me, and I can give them some exercises. The course will involve some computational work, and I will help students setup a computational environment using Python Notebooks.

Lecture notes will be posted below as they are developed (a complete draft of the notes for the whole course will hopefully be posted before classes begin). Homework will be assigned each class, and students will have 1 week to complete it. I highly recommend that all students, including auditors complete the homework. Some key parts of the instruction will be through these exercises, rather than through the lectures.

The lecture notes will somewhat follow Supriyo Datta's Quantum transport: atom to transistor, which will be a useful reference. Datta has a previous book entitled "Electronic Transport in Mesoscopic Systems" which is also relevant.

To save some coding will make some use of the "kwant" quantum transport package, which implements some of the ideas that we will discuss. We will not be using this as a "black-box," rather it will be something that we turn to in order to rapidly "scale-up."

Lecture Notes

• All notes and homework problems, with solutions are in: transport.pdf.
• Instructions for finding the lab room, and for setting up your computer can be found here.
• Notebook for first computer lab (Feb 4, 4pm): Lab 1 Notebook .
• Notebook for second computer lab (Mar 4, 4pm): Lab 2 Notebook .