Unit name | Magnetism and Superconductivity |
---|---|

Unit code | PHYSM0038 |

Credit points | 10 |

Level of study | M/7 |

Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |

Unit director | Dr. Sven Friedemann |

Open unit status | Not open |

Pre-requisites |
N/A |

Co-requisites |
None. |

School/department | School of Physics |

Faculty | Faculty of Science |

**Description**

This course explores the basics of magnetism and superconductivity as well as links between the two. Both are fascinating topics in condensed matter physics linked to many intriguing phenomena and applications like magnet resonance imaging in medicine and magnetic storage in computing.

We use basic quantum mechanical models of atoms, ions, and metals to derive theoretical concepts that show why magnetism and superconductivity occur. We discuss how the key characteristics of magnetism and superconductivity are apparent in these models. We perform some hands-on demonstrations in the lectures which can be linked back to these models.

**Overview of Aims**

- To introduce modern quantum mechanical theories of magnetism and superconductivity.
- To show how quantum mechanics can explain the important experimental phenomena and make quantitative predictions of experimental observables.
- To introduce, where possible, topics of current research interest, such as high temperature superconductivity and advanced magnetic materials.

**Outline syllabus**

Electrons in bands:

Electronic band-structure. Tight binding approximation. Screening and the Mott transition.

Magnetism:

Diamagnetism, paramagnetism. Hund's rules, crystal field effects. The exchange interaction. Weiss’ mean field model of ferromagnetism. The Stoner band model of ferromagnetism. Antiferromagnetism. Spin waves.

Superconductivity - Basic features:

Zero resistance, critical temperatures and fields, Type I and II behaviour. The Meissner-Ochsenfeld effect. Thermodynamics. Electrodynamics; the London theory, flux quantization, penetration depth and coherence length. The origin of the attractive interaction, electron-phonon interaction, isotope effect.

Superconductivity - Microscopic BCS theory:

Cooper pairs, BCS wavefunction, variational solution, quasiparticle excitations, density of states. High temperature superconductors: electronic structure, d-wave superconducting gap, unconventional superconductors (non-phonon pairing), fluctuation effects. Single particle quasiparticle tunnelling, Josephson effect and its application in SQUIDs, and Shapiro steps.

Students should obtain an overview of both magnetism and superconductivity. They should know the main experimental facts defining the physics of magnetism and superconductivity, and be familiar with the standard terminology.

Students should be able to identify which form of magnetism is to be expected for a given material. Students should also be able to perform standard calculations for basic models of magnetism and superconductivity. This includes the models of magnetism in atoms and ions, Hund’s Rules, magnetism in metals, mean-field theory of magnetic order, Stoner model of magnetism, the Hubbard model, and quantum and classical models of spin waves.

Students should be able to explain the properties of superconductors with reference to the theoretical frame work including London theory, basic thermodynamics, and BCS theory of superconductivity. They should be able to explain the microscopic mechanism of superconductivity and should be able to reproduce quantitative predictions and make calculations of thermodynamic, transport, and magnetic properties of superconductors. Students should be able to explain the characteristics of unconventional superconductivity with reference to the gap equation.

The unit will be taught through a combination of

- asynchronous online materials, including narrated presentations and worked examples
- synchronous group problems classes, workshops, tutorials and/or office hours
- asynchronous directed individual formative exercises and other exercises
- guided, structured reading

Coursework Assessment: Problems sheets (20%)

Summative Assessment: Written, timed, open-book examination (80%)

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. PHYSM0038).

**How much time the unit requires**

Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

**Assessment**

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an
assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).

The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.