| Instructor: | Olexei Motrunich
Office: Sloan Annex 127 Phone: (626) 395-8894 Email: motrunch /at\ caltech |
|---|---|
| Class Meets: | Tue, Th 13:00 - 14:30, Lauritsen 269 |
| Office Hours: | Mon 3:00-4:00. |
| Teaching Assistant: | Rory Perkins
Office: 130 Watson e-mail: rory@its.caltech.edu Office hours: Wed 4:00-5:00 |
| Textbook: | Neil W. Ashcroft and N. David Mermin, Solid State Physics
(referred to as A&M), recommended but not required M. Mardar, Condensed Matter Physics, recommended but not required Michael Marder's web page also contains pointer to his lecture notes on the Nicenet. |
| Other Texts: | J. Ziman, Principles of the Theory of Solids
C. Kittel, Introduction to Solid State Physics |
| Homework and Grading: |
There will be a weekly homework assignment posted on Tuesday
and due on Thursday nine days later. Grades will be based on homework (60%) and the final exam (40%) |
PROBLEM SETS:
Course Description:
This is an introductory course in Solid State Physics, emphasizing
the revolution brought in our understanding of material properties
by the advent of quantum mechanics. The focus will be on concrete
physics problems and concepts. While covering standard topics,
the course will also touch upon more recent advances such as
localization and quantum Hall effect.
Topics:
1) Phonons in solids
2) Drude and Sommerfeld theories of metals
* Landau levels and Quantum Hall effect
3) Electrons in periodic potential, band structure,
metals and insulators
* Anderson localization
4) Interacting electron gas, Hartree-Fock approximation;
Quasiparticles
5) Magnetism, magnetic interactions and ordering
Phy135b 2007 course plan
Prerequisites:
Basic quantum mechanics, including spin, the hydrogen atom, and
perturbation theory; basic statistical mechanics and quantum statistics.
Links to other materials on the web
Chetan Nayak's lecture notes for Intro Solid State
LECTURES:
| Lecture 1: | Intro. Solids and Phonons: harmonic chains; normal modes. Required reading: A&M Ch 22, 23. or Marder Ch. 14 Suggested reading: A&M Ch 19, 20., Marder Ch. 15 P. W. Anderson's "More is Different" viewpoint is as vibrant and relevant as it was more than 30 years ago. |
|---|---|
| Lecture 2: | Phonons in 3d. Thermodynamics.
Absence of crystalline order in low dimensions. Required reading: A&M Ch 22, 23. or Marder Ch 14 Suggested reading: The following handouts from Peter Young's course page are very instructive to peruse: "Phonon density of states: fcc lattice" , "Specific Heat: fcc lattice" , and "Debye-Waller factor" . |
| Lecture 3: | Crystal lattices; the reciprocal lattice and diffraction.
Required reading: A&M Ch 4, 5, 6 (pp.96-104) or Marder Ch 1,2,3 |
| Lecture 4: | Drude-Sommerfeld theory of metals. Pauli spin paramagnetism.
Required reading: A&M Ch 1, 2 Suggested reading: The Development of the Quantum Mechanical Electron Theory of Metals: 1900-28 . This is just one of the wonderful collection of historical articles on The Beginnings of Solid State Physics , Proceedings of the Royal Society of London, A, Vol. 371, No. 1744 (1980). |
| Lecture 5: | Pauli spin paramagnetism and Landau diamagnetism; Landau levels.
Lecture notes: Landau diamagnetism Required reading: A&M pp. 661-666 or Marder Ch. 25 Suggested reading: K. Huang, Statistical Mechanics, pp. 253-266; Landau & Lifshitz, v.5 Statistical Physics, pp. 171-175; Franz Wegner's lecture notes pp. 47-52 (in German). |
| Lecture 6: | Magneto-oscillations.
Hall efect in Drude theory. Integer quantum Hall effect. Required reading: see Lecture 5; also A&M Ch 1, Ch 14 pp 264-272 Suggested reading: see also introductory chapters of Lecture Notes on the integer and fractional quantum Hall effects by S. Girvin |
| Lecture 7: |
Electrons in periodic potential. Bloch's theorem Required reading: A&M Ch 8,9,10 or Marder Ch. 7, 8 |
| Lecture 8: | Electrons in periodic potential. Tight-binding method. Required reading: A&M Chs 8,9,10 or Marder Ch. 7, 8 |
| Lecture 9: | Kronig-Penney model. Nearly free electrons in periodic
potential. Required reading: A&M Chs 8,9,10 or Marder Ch. 7, 8 |
| Lecture 10: | General characterization of the bands.
Semiclassical equations for electron dynamics, Bloch oscillations, holes.
Required reading: A&M Ch 12 or Marder Ch 16 |
| Lecture 11: | Semiclassical motion in magnetic field;
cyclotron resonance;
de Haas-van Alphen effect as a Fermi surface probe.
Required reading: A&M Ch 12; Ch 14, pp. 264-274; Ch. 28, pp. 568-572 or Marder Ch. 16 Suggested reading: Many examples of band structures (from Harry Atwater's 2007 lectures) |
| Lecture 12: | Introduction to Anderson localization.
|
| Lecture 13: | Electron-electron interactions. Hartree and Hartree Fock;
Notion of the exchange correlation hole;
Koopman's theorem; HF for Jellium
Required reading: A&M Ch 17 or Marder Ch 9. Lecture notes: Hartree-Fock |
| Lecture 14: | Hartree-Fock for Jellium; HF energy as a function of r_s;
notion of the Wigner crystal.
Ferromagnetic instability in Hartree-Fock and general idea of "mean
field" treatment.
Required reading: A&M Ch 17 or Marder Ch 19 |
| Lecture 15: | Thomas-Fermi for screening. Kohn-Sham scheme for ab-initio
calculations.
Start effective medium for general interactions and dynamical response;
Required reading: A&M Ch 17; A&M Ch 1, pp 16-20 or Marder Ch 19 Lecture notes: Thomas-Fermi screening |
| Lecture 16: | Thomas-Fermi for general interactions and dynamical response;
plasmon for Coulomb and sound mode for short-range interactions.
Landau argument for quasiparticle lifetime.
Required reading: A&M Ch 17; A&M Ch 1, pp 16-20 or Marder Ch 19 Lecture notes: Landau's argument; Heitler-London theory for H_2 molecule |
| Lecture 17: |
Heitler-London theory for H_2 molecule; towards Mott insulators
and Heisenberg spin model. Ferromagnets and antiferromagnets.
Required reading: A&M Ch 32 or Marder Ch 26. |
| Lecture 18: |
Ferromagnets and antiferromagnets -
mean field description and different behavior of susceptibility.
Quantum ferromagnet - spin waves and low-temperature properties.
Quantum antiferromagnet - brief overview.
Required reading: A&M Ch 33 or Marder Ch 26 Lecture notes: Magnetic systems |