Course Description

What are the electrical and thermal conductivity properties of metals and how can one explain these from fundamental principles? How can one unearth the structure of a salt crystal? How do semiconductors and liquid crystals work? What are the properties of glasses? How can one construct a quantum dot? Questions like these, asking about the bulk properties of solids and liquids fall within the scope of condensed matter physics.

Condensed matter attempts to describe the physical properties of bulk materials, frequently starting from fundamental physical principles. The field weaves together principles from quantum mechanics, statistical physics, thermodynamics and electromagnetism and applies these to describe properties of real materials.

What started as an investigation of relatively esoteric conduction properties of metals at low temperatures in the early 20th century has now branched into the largest and most diverse field of physics. Condensed matter physics, with its emphasis on properties of materials, is perhaps the most practical of all physics subfields and lies behind the rapid development of most new information processing technologies.

This course will introduce you to fundamental topics in the traditional areas of condensed matter physics, concentrating on crystalline materials. However, we will also discuss some recent developments in the understanding of non-crystalline solids and liquids.


Course Number: PHYS 309

Instructor: Prof. David Collins, Physics Department

Contact Information:

Class Times: MWF 9:00 - 9:52am

Classroom: Olin 264

First Class Meeting: Wednesday 18 January 2006.

Prerequisites: PHYS 222

Text: M. Ali Omar, Elementary Solid State Physics, Addison Wesley (1993).

First Day Handout: Postscript Format Pdf Format

Outline: Postscript Format Pdf Format

Syllabus

The following is subject to change.

  1. Crystal structure and diffraction in crystals.
  2. Lattice vibrations, phonons.
  3. Electrons in metals, electrical and thermal conductivity.
  4. Energy bands in metals.
  5. Selected special topics from: semiconductors, superconductivity, magnetism.

Homework Assignments

The following will be updated during the semester.

Homework 1 Due: 23 January 2006 Postscript Pdf
Homework 2 Due: 1 February 2006 Postscript Pdf
Homework 3 Due: 6 February 2006 Postscript Pdf
Homework 4 Due: 13 February 2006 Postscript Pdf
Homework 5 Due: 27 February 2006 Postscript Pdf
Homework 6 Due: 21 March 2006 Postscript Pdf
Homework 7 Due: 31 March 2006 Postscript Pdf
Homework 8 Due: 11 April 2006 Postscript Pdf
Homework 9 Due: 18 April 2006 Postscript Pdf
Homework 10 Due: 25 April 2006 Postscript Pdf

Homework Solutions

Homework solutions will be posted on the Blackboard course pages.

Exams

There will be two hour long exams during class on the following dates Monday 20 February and Monday 3 April.


Term paper

You will have to write a 10 to 15 page term paper and give a 25 minute presentation in class, on a topic from the field of condensed matter physics that was not covered during the classes. The term paper will be due by the last day of classes and the presentations will take place during the last week of classes. You must select a topic by Monday 13 February and submit an outline of the paper to me by Monday 27 March.

Useful resources for material include:

  1. Nobel prizes have been awarded for many developments in condensed matter physics. The official Nobel prize web site contains detailed information on these innovations, much of it aimed at a general audience. This would be a good place o get a quick idea of the significance of these developments.
  2. There are a few general articles and useful links at the Institute of Physics' best of condensed matter site.
  3. The are some useful links to review articles at the The Net Advance of Physics. These review articles are mostly posted on the arXiv preprint server. Some are specifically of a pedagogical nature. This is an excellent resource.
  4. Other condensed matter texts, particularly those by Ashcroft & Mermin and Marder.
  5. Physics Today has review articles intended for a general physics audience. These are usually less technical than those of Reviews of Modern Physics.
  6. The American Journal of Physics contains articles with a pedagogical focus. Many of these should be accessible to undergraduates.
  7. Reviews of Modern Physics has technical review articles intended for physicists. This is what practicing physicists use to learn about new developments. The easiest way to search this journal is via PROLA.
  8. Reports on Progress in Physics is similar to Review of Modern Physics.

Possible topics are listed below (under construction).

  1. Scanning tunneling microscopy and surfaces: STM uses the tunneling feature of quantum mechanics to probe surfaces at the atomic level. Development of such microscopes began in the 1980s and these have been vital in learning about the structure of crystalline surfaces.
  2. Atomic force microscopy and surfaces: This technique is similar to STM but uses the motion of a microscopic cantilever to determine the atomic structure of a surface.
  3. Quasicrystals: Certain crystal symmetries are prohibited for the types of lattices that we discussed in class. However, some of these such have actually been observed. A theory of such quasicrystals has been developed and scattering from them has been observed in the last twenty years.
  4. Alloys: Alloys are combinations of metals whose regular crystalline lattices become intertwined. People have deliberately constructed alloys and used them for thousands of years.
  5. Glasses: Glasses do not display a regular crystalline structure but are not liquids either. Little is known about the characterization of glasses.
  6. Liquid crystals: Liquid crystals occupy a territory somewhere between liquids and solids. Unlike solids, they are disordered in some respects but unlike liquids they retain long range order with respect to the orientation of individual molecules. Liquid crystals have polarization properties which have commercial applications in displays.
  7. Superfluids: At very low temperatures, liquid Helium displays an variety of unusual fluid flow properties, in some instances flowing with no measurable resistance. There are several phases of such superfluid helium and detailed theories have been developed to describe their properties.
  8. Quantum Hall effect: The Hall effect has to do with the effect of magnetic fields on the motion of charges within circuits and was originally used to determine whether the moving charges were positive or negative. In certain circumstances the electrons behave as a collective two dimensional fluid and effect is quantized. This has led to the development of very precise ways of measuring resistance.
  9. Neutron scattering in condensed matter physics: Neutrons can scatter off crystal lattices just as X-rays do. However, neutrons can be used to reveal the oscillatory properties of the lattice.
  10. Phase transitions and order in complex systems (e.g. polymers or liquid crystals): Certain complex systems such as magnetic materials or liquid crystals display phases in which their is a high or low degree of order. The extent of this order can characterize the bulk properties of the system. A set of very general and widely applicable laws has been developed in this context.
  11. Superconductivity: At very low temperatures, certain metals conduct with no resistance. A detailed theory (BCS) describes this. In the last 20 years a new class of higher temperature (~100 K) superconductors have emerged. Superconductors are used to provide extremely strong magnetic fields, such as those required in MRI or magnetic levitation.
  12. Tunneling in superconductors, Josephson junctions and SQUIDS: The Josephson effect has to do with charge tunneling through an insulating barrier which separates two superconductors. It is possible to build and characterize such Josephson junctions. These evidently offer a macroscopic form of quantum mechanical variable and have been proposed as building blocks for quantum computers. A SQUID is a particular circuit built from Josephson junctions that is very sensitive detector of magnetic flux.
  13. Quantum dots: Quantum dots are "artificial atoms" built from various semiconducting materials. In recent years these have been constructed and characterized. Some are promising candidates for realizations of quantum computers.
  14. Optical properties of crystals: Since light is an electromagnetic wave, it will interact with electrons in materials. This provides one way of assessing properties of crystals and semiconductors and can lead to practical applications such as solar cells.
  15. Semiconductors: Semiconductors and the devices that are constructed from them form the basis of modern information technology.
  16. Polymers: Polymers are long chain molecules. In solution, they can affect fluid flow properties and there are models for understanding this.

Supplementary Reading

Additional texts which you may find useful are listed below.

  1. General Texts

    1. C. Kittel, Introduction to Solid State Physics, Wiley (2005).

      Kittel's text is widely used as in undergraduate condensed matter courses and would be a reasonable alternative to Omar. The coverage of the material is at a similar level and the problems are comparable.

    2. J. R. Christman, Fundamentals of Solid State Physics, Wiley (1988).

      Unfortunately out of print, although the library has a copy, this is an excellent undergraduate level text. More clearly written than Kittel and more current than Omar.

    3. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Saunders College Publishing (1976).

      Ashcroft and Mermin has been the standard introductory graduate level text although parts of it are accessible to undergraduates. Very well written and laid out, proponents of this text have claimed that it is so good that there has been no need for revision since 1976!

    4. M. P. Marder, Condensed Matter Physics, Wiley (2000).

      This could become the new standard for introductory graduate level texts. Excellent coverage of recent topics.

    Links and Animations

This page is maintained by David Collins
Last modified: 7 February 2006