Description

The module will apply much of the core physics covered in PHY2021, PHY2024, and PHY3051 to novel systems and engage with fundamental electric, magnetic and optical phenomena in metals and dielectrics. The module illustrates and draws on research undertaken in the Department: studies of the metal-to-insulator transition, oscillatory effects in strong magnetic fields, optical and magnetic phenomena.

Module Aims

The module aims to develop understanding of effects that played a key role in the development of contemporary solid state physics and to provide a general description of its current trends. The different topics covered will be linked by the idea that electrons in solids can be treated as quasi-particles interacting with other quasi-particles: electrons, phonons, photons. In addition to electrons, other excitations in solids are considered, e.g. Cooper pairs, plasmons and polaritons.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. develop the concept of energy bands in the tight-binding approximation and compare the outcome of this methodology with the nearly-free electron model described in PHY2024;
  2. explain how the conducting properties of metals are affected by disorder and electron-electron interactions, and describe the types of the metal-to-insulator transition;
  3. explain the significance of complex Fermi surfaces for transport properties of metals and how the shape of the Fermi surface can be mapped using oscillatory effects;
  4. develop classical and quantum mechanical descriptions of the electron motion in electric and magnetic fields, Hall and magnetoresistive effects;
  5. explain characteristic features of superconductors and the origin of superconductivity;
  6. explain how interaction effects modify the properties of quaisi-paricles in solids and descripe the origin of different excitations: plasmon, polariton, polaron, exciton and magnon;
  7. explain the origin of the fundamental magnetic phenomena and the basic models in their description;
• Discipline Specific Skills and Knowledge:
  8. apply core physics to the solution of problems involving unfamiliar systems;
• Personal and Key Transferable / Employment Skills and Knowledge:
  9. use spatial reasoning to derive qualitative solutions to problems;
  10. manage the own work.

Syllabus Plan

1. Electrons in Solids
   1. Calculations of Band Stucture
      1. Tight-binding
      2. Comparison of tight-binding with the nearly-free electron model
      3. Brief introduction to other methods, e.g. LCAO, Pseudo-potentials, LMTO, LAPW
   2. Fermi Surface and Electron Dynamics in Metals.
      1. Construction of the Fermi surface and Fermi surfaces of some metals.
      2. Semiclassical model of electron dynamics. Electron motion in crossed magnetic and electric fields.
      3. Hall effect and magnetoresistance.
      4. Landau quantisation of the electron spectrum.
      5. Shubnikov-de Haas and de Haas-van Alphen effects, experimental conditions for their observation.
      6. Mapping of the Fermi surface in three-dimensional metals.
      7. Metal-to-insulator transition in three- and two-dimensional metals. Current situation in the field.
      8. Electron-electron interaction in metals: Fermi liquid
   3. Superconductivity
      1. Difference between 'ideal' metal and superconductor. Specific features of magnetic, thermal and optical properties of superconductors.
      2. Isotope effect. The concept of the Cooper pair and the outline of the Bardeen-Cooper-Schrieffer (BCS) theory.
      3. Josephson effects. High-temperature superconductivity.
2. Electrons, Phonons and Photons
   1. Dispersion relation for electromagnetic waves in solids and the dielectric function of the electron gas.
   2. Plasma optics and plasmons.
   3. Dielectic function and electrostatic screening. Screened Coulomb potential.
   4. Phonon-photon interaction: polaritons.
   5. Electron-phonon interaction: polarons.
   6. Interband transitions
   7. Electron-hole interaction: excitons.
   8. Raman Spectra
3. Quasiparticles in Low-dimensional Solids
   1. Excitons, plasmons, polarons, and polaritons
   2. Graphene
4. Magnetic Properties of Solids
   1. Ferromagnetism and antiferromagnetism.
   2. Spin waves and magnons.
   3. Giant magneto-resistance.

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Kittel C. (2005), Introduction to Solid State Physics (8^th edition), Wiley, ISBN 978-0-471-41526-8

Supplementary texts:

• Ashcroft N.W. and Mermin N.D. (1976), Solid State Physics, Holt-Saunders, ISBN 0-03-083993-9
• Burns G. (1985), Solid State Physics, Academic Press, ISBN 0-12-146070-3
• Hook J.R. and Hall H.E. (1991), Solid State Physics (2^nd edition), Wiley, ISBN 0-471-928054

ELE:

• http://newton.ex.ac.uk/redirects/ELE/phym003

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: See Physics Assessment Conventions.

KIS Data Summary

Miscellaneous