Superconductivity
Supraledning

FFFN40, 7.5 credits, A (Second Cycle)

Valid for: 2025/26
Faculty: Faculty of Engineering LTH
Decided by: PLED F/Pi
Date of Decision: 2025-04-10
Effective: 2025-05-05

General Information

Depth of study relative to the degree requirements: Second cycle, in-depth level of the course cannot be classified
Elective for: E4, F4, F4-nf, F4-tf, F4-kv, MFOT1, MNAV1, N4-nf
Language of instruction: The course will be given in English

Aim

The course aims to teach the fundamental theoretical concepts behind superconductivity. Students will also learn to apply analytical and numerical methods to investigate simple phenomena in superconductors based on the London equations, Ginzburg-Landau theory, and BCS theory. Additionally, they will gain basic knowledge of various methods for experimentally studying the properties of superconducting materials. The course will also provide insight into the use of superconductors in some technical applications, with a particular focus on quantum computers and other quantum technologies.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to explain the fundamentals behind phenomenological theories of superconductivity (London and Ginzburg-Landau) and how to derive the central equations in these theories based on thermodynamic arguments.
• be able to describe the key steps in deriving the microscopic theory of superconductivity (BCS theory), how these equations give rise to a superconducting gap and the fundamental excitations in a superconductor, as well as simple theories for transport in systems with a superconductor coupled to a metal.
• be able to explain the relationship between current and phase difference in a Josephson junction.
• be able to describe how phase coherence in Josephson junctions can be utilized in various superconducting qubits, especially in so-called Cooper pair boxes and transmons.
• be able to provide an overview of how to experimentally investigate the properties of a superconducting material, such as the gap and coherence length.
• be able to discuss some more advanced concepts, which may vary depending on students' choice of projects. Examples include high-temperature superconductors, topological superconductors, superconducting logical circuits, and how to connect many superconducting qubits in a quantum computer.

Competences and skills
For a passing grade the student must

• be able to apply various (phenomenological and microscopic) theories of superconductivity to qualitatively, analytically, and numerically describe specific properties and phenomena within superconductivity.
• be able to apply their knowledge of basic theories of superconductivity to understand superconducting qubits.
• be able to demonstrate the ability to comprehend a more advanced topic within superconductivity and convey this knowledge in an educational manner to other students.

Judgement and approach
For a passing grade the student must

• be able to search for scientific literature and identify material relevant to the course projects.
• be able to convey advanced scientific material to other students in a lecture that maintains a high pedagogical standard.

Contents

The course covers:

• The fundamental theoretical descriptions of the superconducting phase and its properties.
• The London equations, type I and type II superconductors.
• Ginzburg-Landau theory as a more advanced version of the London equations.
• Microscopic theory of superconductors (BCS theory), superconducting gap, fundamental excitations, and transport in circuits with coupled superconductors (Josephson junctions) and with superconductors coupled to metallic contacts.
• Superconducting circuits, Coulomb blockade, and various types of superconducting qubits.
• A selection of in-depth topics in the form of student projects (varies based on students' interests).

The teaching consists of lectures and student-led lectures. Attendance at the studentled lectures is mandatory.

Examination details

Grading scale: TH - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment:

The course is assessed through assignments, student-led lectures, and an oral examination. Attendance at student-led lectures is mandatory. Approved assignments are required to be eligible for the oral examination, which is based on the solutions to the assignments. Students who do not pass the regular examination are offered an additional examination opportunity shortly thereafter.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Modules
Code: 0124. Name: Project.
Credits: 2.0. Grading scale: TH - (U, 3, 4, 5). Assessment: Oral presentation.
Code: 0224. Name: Hand-in Exercises.
Credits: 2.0. Grading scale: UG - (U, G). Assessment: Written solutions to problems.
Code: 0324. Name: Oral Examination.
Credits: 3.5. Grading scale: TH - (U, 3, 4, 5). Assessment: Oral exam.

Admission

Assumed prior knowledge: Knowledge of quantum mechanics corresponding to FMFN01 Quantum Mechanics, Advanced Course 1, 7.5 credits, knowledge corresponding to FAFF55 Atomic Physics, 6 credits, and knowledge corresponding to FFFF01 Electronic Materials, 7.5 credits, or FFFF05 Solid State Physics, 7.5 credits.
The number of participants is limited to: No

Reading list

• Handouts.
• Annett, James F: Superconductivity, superfluids, and condensates. New York : Oxford University Press, 2004, ISBN: 0198507550.

Contact

Course coordinator: Martin Leijnse, martin.leijnse@ftf.lth.se
Examinator: Martin Leijnse, martin.leijnse@ftf.lth.se
Course homepage: https://canvas.education.lu.se/

Further information

The course is in full coordinated with FYST84 Superconductivity, 7.5 credits, which is a course given at the Faculty of Science.