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 course will be taught in eighteen lectures with calculations and derivations presented as "chalk and talk" on the blackboard (whiteboard). The more evolved derivations are available to download as videos for revision outside the lectures – these can be paused for learning at individual pace. An overview of the lectures is available as powerpoint slides to download. Very detailed lecture notes are published on the Blackboard website in advance of the lectures. Several problem sets are set with 1-2 weeks time for students to attempt these. Two two-hour problem classes will be used to discuss the problems. Discussions and revisions are available before the examination.

Formative Assessment:

Problem sheets provide formative feedback.

Summative Assessment:

2 hour written exam (100%)

Blundell, Magnetism in condensed matter physics (OUP Oxford)

**Other useful texts**

Ibach and Luth, Solid State Physics (Springer-Verlag)

Kittel, Introduction to Solid State Physics (Wiley)

Ashcroft and Mermin, Solid State Physics (Holt, Rinehart, Winston)

Tilley and Tilley, Superfluidity and Superconductivity (Hilger)

Tinkham, Introduction to Superconductivity (McGraw-Hill)