David Tong: Solid State Physics

David Tong: Lectures on Solid State Physics

This is an introduction to solid state physics. It covers the basics of band structure, Fermi surfaces, phonons, and particles in magnetic fields. Please do email me if you find any typos or mistakes.

PostScript      PDF

Cambridge students: This material is contained as part of the lectures on Applications of Quantum Mechanics.


  • 1. Particles in Magnetic Fields:   PDF
    Gauge field, gauge transformation; Landau levels, degeneracy; Aharonov-Bohm effect; Magnetic monopoles, Dirac quantisation; Spin in a magnetic field, spin precession.
  • 2. Band Structure:   PDF
    Electrons in one dimension, tight-binding, nearly free electrons, Floquet matrix, Bloch's theorem; Bravais lattices, cubic, BCC and FCC, the Wigner-Seitz cell, the reciprocal lattice, the Brillouin zone; band structure, crystal momentum, crystallographic notation, nearly free electrons in 3d, tight-binding in 3d; Wannier functions, localised and extended stats, LCAO
  • 3. Electron Dynamics in Solids:   PDF
    Fermi surfaces, metals vs insulators, graphene; Bloch electrons; effective velocity and mass, semi-classical equations of motion, Bloch oscillations, holes, Drude model; magnetic fields, cyclotron frequency, Onsager quantisation, de Haas-van Alphen oscillations.
  • 4. Phonons:   PDF
    Monotonic chain; diatomic chain, optical and accoustic bands, Peierls instability; Quantization; Field theory.

Problem Sheets

(for the Applications of Quantum Mechanics course.)

  • Problem Sheet 1:   Postscript    PDF    Scattering

  • Problem Sheet 2:   Postscript    PDF    Variational Method, 1d Band Structure

  • Problem Sheet 3:   Postscript    PDF    3d Band Structure; Fermi Surfaces   

  • Problem Sheet 4:   Postscript    PDF    Phonons; Particles in a Magnetic Field

Solid State Physics on the Web