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Graduate courses

Departments' graduate courses for PhD-students.


Syllabus for

Academic year
FMI036 - Superconductivity and low-temperature physics
Syllabus adopted 2011-02-22 by Head of Programme (or corresponding)
Owner: MPNAT
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Engineering Physics

Teaching language: English
Open for exchange students
Block schedule: D

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0103 Examination 7,5 c Grading: TH   7,5 c   12 Mar 2013 pm V,  14 Jan 2013 pm M,  22 Aug 2013 pm V

In programs

MPNAT NANOTECHNOLOGY, MSC PROGR, Year 1 (compulsory elective)


Professor  Per Delsing

Course evaluation:

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For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

A basic course in quantum mechanics (i.e. FUF040), and a basic course in solid state physics/electronics (i.e. FFY011).


Physical phenomena are often studied at low temperature, particularly within condensed matter physics. Coherence effects become dominating. The course contents are concentrated to a few sub-fields: 1. studies of superconductors (about half the time), both an understanding of superconductivity starting from microscopic properties and of macroscopic quantum effects, particularly the Josephson effects; 2. properties of superfluid helium and Bose-Einstein condensates, i.e. of macroscopic quantum fluids; 3. mesoscopic effects, for example single electronics 4. low temperature techniques, i.e. a summary of different cooling methods, thermal properties of materials, thermometry, etc. One purpose is to meet models that can be applied to other fields of Physics. The course is suitable for those that want to continue doing research in Physics.

Learning outcomes (after completion of the course the student should be able to)

Explain the basic properties of both high Tc and low Tc superconductors.
Apply Londons equations to superconductors to explain their electromagnetic properties.
Describe thermodynamic properties of superconductors
with the help of Ginzburg Landau theory describe different lengthscales such as the penetration depth and the coherence length, and explain the differences between type I and type II superconductors.
Account for the basic ideas of the BCS theory, like Cooper-pairing, energy gap and the density of states for exitations.
Describe the phase diagrams for both helium-3 and helium-4.
Describe how Bose-Einstein condensation comes about.
Describe superfluid phenomena such as, rollin film, the fountain effect and second sound.
Describe different cooling methods which are used both above and below 1 Kelvin.
Explain physical properties of different materials at low temperature.


The course may be considered as an application of courses in quantum physics, solid state physics, electrodynamics and thermodynamics.
The course has three parts:

Basic properties of superconductors, thermodynamics, superconductors in magnetic fields
The London equations, electromagnetic properties, penetration depth
Ginzburg-Landau theory, coherence length, type I and type II superconductors
BCS theory, second quantization, Cooper-pairing, energy gap
Tunneling, Josephson effects and SIS tunneling
High Tc superconductors, structure, d-wave symmetry, phase diagram,
Overview of applications, squids, microwave devices, power applications

Properties of liquid helium-4, the phase diagram, superfluidity
Superfluid phenomena, rollin film, fountain effect, second sound
Exitations and vortecies in superfluids
Properties of liquid helium-3, the phase diagra, superfluidity
Symmetry properties of superfluid helium-3

Themal and electrical properties for different materials at low temperature
Cooling methods above 1K, Joule-Tomphson, Gifford-McMahon, evaporation cooling
Liquefication of helium
Cooling methods below 1K, dilution refrigeration, adiabatic demagnetisation, Pomerantchuck cooling


The course embraces lectures (about 30 hours), two laborations (Josephson effect, and superfluid helium)and home exercises.


J.R. Waldram: Superconductivity of metals and cuprates
(Institute of Physics Publ., Bristol, 1996, pbk)
Lecture notes.


The course ends with a written exam. There is a laboratory part that must be taken.

Page manager Published: Thu 04 Feb 2021.