The final project provides you with an opportunity
to investigate some issues in solid state or condensed matter physics of
particular interest to you. The project involves selecting an interesting area,
a specific topic, and writing a short paper that describes how to use some of
the concepts from the course to understand a particular physical effect,
device, or process. Your paper should contain at least one example of a
calculation, to show either how to semiquantitatively explain or how simple
standard physics FAILS to explain the topic of interest.
I have provided a list of some general project
topics below. However, this list is only suggestive. I strongly encourage you
to select a topic that is of direct importance in your graduate research. The
best projects come if you have a burning desire to study a specific topic. Try
not to limit yourself to the topics listed unless one of them looks
interesting.
Regardless of topic area, the project involves three
pieces
Imagine writing your paper, not for me, but for someone else in the class. Even better, I'd recommend that you imagine addressing your paper to Yourself, but with your state of knowledge reset to where it was at the beginning of the course. In other words, hit the high points about the solid state ideas that you need to understand the topic, and help the reader to actually understand how these ideas explain what is happening. You don't need to produce elegant new derivations. Instead, try to provide a clean description of something that interests you. I particularly like papers that explain interesting problems that could be used for long homeworks!
An outline of your proposed paper is due on Friday, April 25. The outline is 25% of the project grade. The outline should include:
· An abstract describing your project, what you are particularly interested in explaining, and how you expect to do so.
· An outline of the major sections of the paper.
· At least five references (books, articles, no more than two websites, other published material) that you expect to use in your paper.
I will read these paragraphs and outlines; I will return comments to you by Mon. April 28 and will attempt to provide guidance, particularly for projects that look too ambitious.
Your paper should be 10-15 pages in length and will be worth 70% of the project grade. The paper must be formatted using some type of word processor. I will not be grading handwritten papers. In addition, papers should include the following:
· A title page with: 1) Title 2) Author 3) An abstract of no more than 300 words that describes the major points in your paper and what you have found. Think of this abstract as a concise description that you could recite to an interested reader to help them decide whether the paper is something that they’d like to read.
· Your original graphs (if any) should include the code used to plot them e.g., Mathematica commands, and either the graphed function or a table of plotted data points. Figures taken from other sources must be referenced in the figure caption. Other technical graphs should be clear enough to allow an interested reader to reproduce the plots themselves.
· A references section with at least five references (might be the same as you used in your outline, or might not), including at least one of each of the following: Books, journal or technical articles, websites, popular magazine articles. You should include appropriate citations to these sources in your text.
The finished papers will be submitted online to Turnitin.com (more details later) and a hard copy should be handed in to me by Friday, May 9, 2003.
1. Linear and nonlinear optical properties.
Lasers have caused a revolution in the study of optical properties of materials. Optics provides a direct way to study the vibrational and electronic energies in condensed matter systems, both in linear and nonlinear response. Therefore, these properties are of extreme importance in studying materials.
Project Suggestions: Pick a particular type of
optical property, say the index of refraction of direct gap semiconductors, and
explain it.
2. Superconductivity or superfluidity
Most of the time, we think of quantum mechanics as
providing us with the wave function of some very small object (say an electron
in a hydrogen atom). However, in superconductors, a huge number of the
electrons work together to fall into one huge quantum mechanical wave function.
The end result is a set of spectacular behaviors such as zero electrical
resistance, the ability to quantize magnetic flux in superconducting rings, the
ac Josephson effect, where the time dependence of the wave function becomes
directly measurable, and vortex structure. Superconductors are the original
'macroscopic quantum system'.
Project Suggestions: Dilute Bose gases, or
describe the NIST 'Josephson Voltage Standard'.
3. Quantum and fractional quantum Hall effect
Two-dimensional electron gases in semiconductor
heterostructures display some genuinely spectacular physics. Interesting
behavior in these systems first appeared in the quantization of the Hall
voltage (thus the name). It is now recognized that electron-electron
interactions lead to quasiparticles with very non-electron properties e.g.,
fractional charge! Much of the physics normally thought to occur only in
relativistic quantum systems like those of QED also appear in fractional
quantum hall systems.
Project Suggestions: Find out about the
fractional ½ state. What’s a skyrmion anyway?
4. Semiconductor Devices
If you want to understand the behavior of modern
electronics, especially integrated circuits, you need to understand some
quantum mechanics. Until quantum mechanics, even the basic issues in the
behavior of metals, insulators, and semiconductors (like why they are even
stable against collapse into the nucleus) could not be understood.
Project Suggestions: Pick an electronic device,
like the silicon field effect transistor, the photo diode, or perhaps the diode
laser (some overlap with the lasers project)
5. Surface Physics and scanning tunneling microscopy
The scanning tunneling microscope allows us to look
at individual atoms and molecules on surfaces, by using quantum mechanical
tunneling. These microscopes, along with a host of related techniques like
atomic force microscopy, have revolutionized the study of surfaces.
Project Suggestions: Explain the tunneling
microscope and give an example of understanding the images from some
particularly interesting molecule or surface.
6. Band structure calculations
Can you understand the electronic energy levels of
your favorite material? Why is GaAs a ‘direct-gap’ semiconductor, while silicon
is not? What is the Fermi surface of high temperature superconducting YBCO
supposed to look like in the independent electron approximation?
Project Suggestions: Pick your favorite
material and see if you can understand the electronic energy levels. What are
Slater-Koster parameters? How can we approximately include electron-electron
interactions?