Topological Materials

Course manual 2022/2023

Course content

This 3EC course will cover basic concepts in the field of topological materials. One of the three major breakthroughs in physics of the 21st century involves the discovery of ‘topological phases of matter’ (2016 Nobel Prize in Physics). This course will cover a wide range of topics from quantum, to magnetic, soft and designer matter. Exciting applications now range all the way from defining the SI unit of resistance to enabling one-way acoustic filters, to elucidating the Earth’s equatorial currents. The course will take you on a conceptual journey starting from basic concepts such as Zak phases, Berry phase and Chern invariants. You will then discover how you can use these basic concepts to understand new phenomena such as protected quantized edge states. Finally, we will focus on current state-of-the-art applications and provide you with an outlook on open research questions.

Objectives

• The student is able to identify fingerprints of topological edge states and topological defects in quantum materials, magnetic materials, soft matter and metamaterials.
• The student is able to explain what topological invariants are.
• The student can calculate Chern numbers.
• The student is able to demonstrate the presence of topological edge states.
• The student is able to explain the role played by time reversal symmetry in fermionic and bosonic topological materials.
• The student is able to explain what topological defects are.
• The student can calculate the critical temperatures of a Berezhinski Kosterlitz Thouless phase transition.
• The student can derive the shape of topological solitons and calculate their topological charge.
• The student can identify topological defects in a given field configuration.

Teaching methods

The lecture slots will consist of combined lectures and in-class tutorials. Additionally, you will be assigned homework and during the course you will work on a short project.

The grading in this course will consist of two components:

1. The first component is based on participation to lectures (via quizzes, reading homework and discussions) and tutorials. This will pass/fail. If you actively participate in all activities during lectures and tutorials you will pass. If you don't manage to do so, you will one opportunity to make up for it via an oral exam in week 4; If you pass this first component, your grade is guaranteed to be at least 7.
2. The second component is based on a project and presentation. You will have to reproduce a computation from a recent scientific article, write a short report and give a presentation about it. This will be done in groups. This component determine the final 30% of your grade.

Both components are required to pass the course. The rationale behind this grading is that you will constantly practice with the material, get a lot of feedback and can monitor how you're doing, but without the pressure of a final exam. This method has been very successfully used in other courses, and we hope you will like it too.

Learning activities

Attendance

Requirements concerning attendance (OER-B).

Assessment

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• dr. Corentin Coulais