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This is the web page for an online special topics course on topological phases that I taught at University of Cologne in the Summer Semester of 2020. The lectures as well as lecture notes are online and can be accessed by following the links below.
During the summer semester of 2020, I am teaching a course on topological phases, aimed towards masters' students, in collaboration with Dr. Ciarán Hickey. My lectures, consisting the first half of this course, will focus on noninteracting fermionic topological phases of matter. In particular, I will talk about topological insulators and their symmetry classification. The second half of this course will focus on interacting topological phases. For more details on this part of the course, check out Ciarán's course webpage.
Topological phases have come to play an increasingly prominent role in condensed matter physics over the last decade. The goal of this course is to expose the audience to some of the theoretical ideas underlying this field, which has come to encompass a broad range of topics and systems of both theoretical and experimental interest.
J. Cham, Nature Physics 11, 799 (2015).
Click here to visit the website for the second half of the course, taught by Dr. Ciarán Hickey.
Click here to visit the website for the second half of the course, taught by Dr. Ciarán Hickey.
Course schedule and logistics
Course schedule and logistics
Owing to the CoViD-19 situation, the semester will start online on Apr 20th. The course consists of a weekly 90 minute blackboard lecture as well as a tutorial session. We will record and upload the lectures a few days before the assigned lecture slots, and organize a Zoom session during the lecture slots (Thursdays, 10:00-11:30) , where we can discuss the lecture and you can ask any questions that you might have about it.
The tutorials will be organized as Zoom sessions, approximately once every two weeks in the usual tutorial slot (Fridays, 12:30-14:00). For every sessions, there will be a few numerical problems pertaining to the previous lectures. The tutorials are intended to complement the more theoretical approach of the lectures with numerical computations, which not only provide a more direct approach to various theoretical ideas, but are also indispensable for conducting research on these topics.
General resources
General resources
There are a lot of great resources on noninteracting topological phases available online in the form of lecture notes or review articles. A similar list for interacting topological phases can be found on Ciarán's website.
The following is a partial list:
Lecture notes by Joel Moore. These follow an approach similar to the present lectures, starting from the mathematical notation of topology and building up to the condensed matter physics notion of topology.
Lecture notes by Ed Witten from the Princeton summer school of '15. These provide a rather lucid and, coming from a string theorist, quite an interesting Martian perspective on topological phases.
The online course on topological phases. This includes short lectures and detailed written notes on various topics as well as source code for various numerical simulations.
Review article by M. Zahid Hasan and Charlie Kane. The classic review on topological insulators, this article covers the ideas in the air in the early days of topological insulators.
A longer review article by Xiao-Liang Qi and Shou-Cheng Zhang. Another early review of topological insulators.
Lectures
Lectures
All video lectures are uploaded to a Vimeo Showcase. The lecture notes can be found here. For more detail on individual lectures, please visit their corresponding webpages linked below:
Tutorials
Tutorials
Logistics
Logistics
The biweekly tutorials would take place as a Zoom meeting, with a brief (~10 min) discussion of the problem statements for the session as well as their relation to what we've seen in the lectures.
I will use the Julia programming language for the tutorials. Julia is a relatively new high-level free/open-source programming language with a syntax similar to Python and MATLAB, but offers performance often comparable to lower level languages. Even if you aren't, it should be pretty straightforward to pick up if you have some familiarity with Python or MATLAB. You are also free to use another programming language if you so prefer. To use Julia for the tutorial, you should install Julia and Jupyter, as well as the Plots package in Julia, before the first tutorial. I have collected the instruction for that as well as some resources for Julia here.
I will post a template Jupyter notebook on the Tuesday evening before each tutorial, which will detail the problem statements with some background information as well as outline the solution. You should read through the template notebook/pdf before the tutorial and familiarize yourselves with the background info on the problems for the week. However, you need not work on the problems themselves in advance, since the main goal of the tutorial is to discuss and work together on the problems during the tutorial slot.
The following links are no longer active!
You can sign up for the course at KLIPS or ILIAS.
If you are interested in attending the lectures but do not want to register for the course, you can sign up to the mailing list by clicking here or by sending me an email at vdwivedi@thp.uni-koeln.de.
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