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Unit information: Condensed Matter 410 - Magnetism and Superconductivity in 2015/16

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Unit name Condensed Matter 410 - Magnetism and Superconductivity
Unit code PHYSM1000
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Antognozzi
Open unit status Not open
Pre-requisites

N/A

Co-requisites

None

School/department School of Physics
Faculty Faculty of Science

Description

Electrons in bands: electronic bandstructure. Tight binding approximation. Screening and the Mott transition. Scattering of electrons in bands. Quantum oscillations and the measurement of Fermi surfaces. Magnetism: different types of magnetic behaviour. Diamagnetism. Paramagnetism. The exchange interaction. The band model of ferromagnetism. Antiferromagnetism. Spin waves.

Superconductivity: introduction; discovery and occurrence. Zero resistance, critical temperatures and fields, Type I and II behaviour. The Meissner-Ochsenfeld effect. Evidence of energy gap; heat capacity, microwave and infra-red properties, tunnelling. Thermodynamics.

Electrodynamics; the London equation, flux quantization, macroscopic wavefunction, penetration depth and coherence length. The origin of the attractive interaction, electron-phonon interaction, isotope effect. Microscopic theory, Cooper pairs, BCS theory. Josephson effect. High temperature superconductors.

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.

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.

Intended learning outcomes

Know the main experimental facts defining the physics of magnetism and superconductivity, and be familiar with the standard terminology. Be familiar with and be able to make calculations using the mean field models of ferromagnetism, antiferromagnetism, paramagnetism and diamagnetism. Be able to use the London and BCS theories of superconductivity to calculate various physical phenomena such as electromagnetism, thermodynamics and tunnelling.

Teaching details

Lectures (18 hours) and problems classes (4 hours).

Assessment Details

Formative Assessment:

Problem sheets provide formative feedback.

Summative Assessment:

A final 2 hour written examination.

Reading and References

  • 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)

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