Supraledning

**Valid from:** Autumn 2019**Decided by:** Anders Gustafsson (ftf-agu), FUN2**Date of establishment:** 2019-09-12

**Division:** Solid State Physics**Course type:** Third-cycle course**Teaching language:** English

The purpose of the course is to make the students familiar with the basic theoretical concepts of superconductivity. They should also be able to use analytical and numerical methods to study basic phenomena in superconductivity based on the London equations, Ginzburg-Landau theory, and BCS theory. The course also gives some basic knowledge of some applications of superconductivity.

*Knowledge and Understanding*

For a passing grade the doctoral student must

- Have a basic understanding of phenomenological theories of superconductivity (according to London and Ginzburg-Landau) and how to arrive at the basic form of the fundamental equations in these theories based on thermodynamic arguments.
- Know the most important steps in the derivation of the microscopic theory of superconductivity (BCS theory). Understand how these equations give rise to a superconducting gap, explain the elementary excitations of a superconductor and can be used to understand phase coherent transport in systems involving superconductors.
- Understand the basics of how the phase coherence of superconducting circuits can be used, for example to make quantum bits.
- Have a basic grasp of some more advanced concepts, such as high-temperature superconductors and/or topological superconductivity.

*Competences and Skills*

For a passing grade the doctoral student must

- Be able to use the different (phenomenological and microscopic) theories of superconductivity to describe specific superconducting properties and phenomena.
- Demonstrate the ability to grasp a more advanced theme within superconductivity and to convey this knowledge in a pedagogical way to fellow students.

*Judgement and Approach*

For a passing grade the doctoral student must

- Demonstrate the ability to search scientific literature and find material that is relevant for the project.
- Demonstrate the ability to convey advanced scientific material to fellow students in a lecture of good pedagogical quality.

The foundations of theoretical descriptions of the superconducting phase and its properties. The London equations and type I and type II superconductors, vortices. Ginzburg-Landau theory as a more sophisticated version of the London equations. Microscopic theory of superconductivity as given by the BCS theory, superconducting gap, elementary excitations and transport in weak superconducting links (Josephson junctions) and in superconducting junctions coupled to normal metals. Some basic applications within superconducting circuits and superconducting qubits.

Annett, James F.: Superconductivity, Superfluids and Condensates. Oxford University Press, 2004. ISBN 9780198507567.

**Types of instruction:** Lectures, exercises, project, self-study literature review

**Examination formats:** Written assignments, seminars given by participants.
For a passing grade, the students should:
- Attend most lectures.
- Complete 3 sets of homework problems (can be done in pairs).
- Do a project related to the course, which is then presented in a lecture-style presentation. Can be done in pairs.
**Grading scale:** Failed, pass**Examiner:**

**Admission requirements:** Course grades showing that the student can be expected to have the assumed prior knowledge (see below).**Assumed prior knowledge:** Most importantly knowledge of quantum mechanics including the concept of second quantization. In addition, students should have taken at least a basic course in each of the following areas: statistical physics and thermodynamics, electromagnetism and solid state physics.**Selection criteria:** Evidence of required prior knowledge (course grades). There is no limitation to the number of participants.

The intention is to give this course every second year, probably always during the full autumn semester. However, the course will only be given if there is a sufficient number of interested students (at least 6-7 students).

**Course coordinators:**