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Syllabus for

Academic year
FMI036 - Superconductivity and low-temperature physics
Owner: FNMAS
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: D

Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0103 Examination 5,0 c Grading: TH   5,0 c   Contact examiner,  Contact examiner

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Professor  Tord Claeson
Professor  Per Delsing
Professor  Dag Winkler


FMI035   Low temperature physics


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

FTF040, 041, 042
FFY010, 011


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.


See above.


The course may be considered as an application of courses in quantum physics, statistical physics, solid state physics, and thermodynamics.

In order to understand the nature of superconductivity, we must apply knowledge from solid state theory. However, we do not know sufficiently well how basic parameters influence the superconducting critical temperature (the transition temperature at which the lectrical resistance disappears) to predict how to fabricate a superconductor with a high critical temperature. Such a material will hahave high technical and economic value. A spectacular breakthrough within the field of superconductivity occurred fifteen years ago. The critical temperature of copper oxides, which have a layer structure, can be well above 100 K. The research in superconductivity is intensive and cross disciplinary, but many aspects are still unknown. The phenomenon has opened up a second generation of knowledge in condensed matter physics. The course treats properties and models of high temperature superconductivity. Quantum mechanics can be applied at a macroscopic scale in superconductors. Interference between electrons that pass Josephson junctions in parallel give currents that depend upon the vector potential in the inscribed area, not only upon electromagnetic fields. The dependence is utilized in hypersensitive instruments and detectors. Aspects of mesoscopic physics, that fall in between atomic and macroscopic physics, are also treated. Single electronics is based upon the control of electrons one-by-one. Fields of Interest: The course can be of interest for a. physicists - many properties can only be studied at low temperature where thermal fluctuations are small. Properties of superconductors and quantum liquids are of great interest from the physics point of view. Cryogenics is an expanding technology; b. electrical engineers - application of superconductivity both within the power sector (transmission of electrical power, motors and generators) and in electronics (sensitive instruments, standards, analogue and digital devices); c. chemical and mechanical engineers - applications of thermodynamics in cooling methods, handling of cryogenes. Practical
applications are considered in the course but the main part of the time is spent on basic physical models that often are valid also in other parts of physics.

Liquid He-3 and He-4 are examples of Fermi and Bose liquids, resp. Spectacular properties of these liquids, for example superfluidity, can be related to specific properties of statistical distributions. Basic thermodynamic laws must be applied to discuss cooling principles.

New, advanced cooling methods give temperatures of the order of nanokelvin. Adiabatic demagnetisation of nuclear spins and laser cooling are examples of refrigeration methods to reach the very lowest temperatures.

Superconductivity: phenomenological models. Type I and type II superconductors. Ginzburg-Landau theory. Microscopic BCS model of superconductivity. Tunneling. Macroscopic quantum effects. Technical applications. High temperature superconductors.
Cooling methods, design of cryostats, thermometry. Superfluidity of liquid helium. He-3 as a Fermi liquid.

It may be mentioned that the
topics of several recent Nobel prizes in Physics (e.g., 1996, 97, 98, 2000, 01, 03) are treated within the course.


Lectures 36h
Two Laborations 4h each
Exercises 2h
Home problems


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


The course ends with a written exam. There is a laboratory part that must be taken. Voluntary home problems give additional points for the exam. Optional term paper and seminar.

Page manager Published: Thu 03 Nov 2022.