CONDENSED MATTER PHYSICS II - Physics 561 Fall 2005

CONDENSED MATTER PHYSICS II

PHYSICS 561 -- Spring 2005

Course web Pages: http://w3.physics.uiuc.edu/~rmartin/561/

Richard M. Martin, Professor

2129 ESB, 333-4229, rmartin@uiuc.edu

Grader: Jiansheng Wu, wu4@uiuc.edeu

Course Description

The purpose of this course is to provide a framework for graduate students to understand at an "advanced" level some of the important aspects of the physics of condensed matter. We will build upon the material typically included in the previous course, Physics 560, which describes many of the important properties of solids in terms of non-interacting independent particles. One goal of the present course will be to start from the basic strongly-interacting particles - nuclei and electrons - and develop a description of condensed systems in terms of “elementary excitations”. Often these excitations can be viewed as weakly interacting so that they lead to many of the properties of non-interacting particles. We will review selected aspects of independent particles - such as the classifications of perfect crystals into metals, semiconductors and insulators - and address the extent to which we can understand such fundamental properties of solids starting from the full interacting many-body system of nuclei and electrons. In order to understand this renormalization to weakly interacting excitations and also to describe experimental measurements made on interacting systems, we will introduce some mathematical methods involving correlation functions and Green’s functions. In addition, cooperative effects among the interacting particles may lead to consequences that cannot be described by independent particles, namely cooperative transitions to new phases of matter, such as the superconducting state, magnetism, metal-insulator transitions, Luttinger liquids and quantum Hall states. We will study such cooperative effects not only because of their central importance in condensed matter but also because they are paradigms for understanding similar phenomena in many fields of science.

The primary emphasis is upon the concepts and general theory. In some cases we will go into sufficient depth to describe current methods that are widely used, such as the GW method for electron addition/removal spectra, the Bethe-Salpeter equation for response functions and dynamical mean field theory for strongly correlated systems. In these cases we will treat example problems and describe representative results for interesting actual cases, such as heavy fermion materials, metal-insulator transitions in transition metal oxides, etc.

The first part of the course deals with the description of interacting systems in terms of “elementary excitations” or “quasiparticles”. We will focus upon the most important qualitative conclusions, such as the nature of the Fermi surface, and the relation to experimentally measurable quantities. The second part is on cooperative phase transitions to states of "broken symmetry" in which there are qualitative changes in the nature of the elementary excitations and "order parameters" describing the new phases. In particular, we will consider superconductivity (the microscopic theory, order parameter and variations in the order parameter) and strongly interacting electrons in transition metal and rare earth compounds, which are of great current interest because of the interesting phenomena they exhibit, including metal-insulator transitions, magnetism, and high-temperature superconductivity. The last section is on the qualitative classification of the states of matter, including current topics of quantum phase transitions and topological transitions.

Background Expected of Students

The background expected of students in this class is a working knowledge of quantum theory (e.g., second quantization, which will be briefly reviewed), elementary complex variables, and knowledge of condensed matter physics at the level of Physics 560. The latter includes the mathematical description of periodic systems, Bragg scattering, common crystal structures, the nature of phonon dispersion curves and electron bands in the Brillouin Zone, one-electron description of the Fermi surface of metals and the bands in semiconductors and insulators, and other similar material covered, for example, in Aschroft and Mermin (A&M), Harrison, or other texts. The type of material I will assume as background is:

	A&M	Harrison
Crystal lattices	3-7	I
Transport and Thermal Properties	1-2	III 1-2
Independent electron bands	8-15	II 1-7
Binding energies of solids	19-20	IV 1-2

Class Schedule

Lectures will be given 10:30-11:50 Tuesday and Thursday. There will be no classes on some occasions. Make-up classes will be announced and will be coordinated with schedules of the students.

Availability of Staff

Office hours will be announced after the start of the semester and posted on the class web pages. We will be pleased to discuss with students at other available times. Please make an appointment by email for times other than the class period or office hours.

Homework

There will be (approximately) six homework sets during the semester. Problems will posted on the class web pagers; solutions will be posted on the web pages if it is feasible for us to have them in electronic form. Otherwise they will be handed out. Solutions to the problem sets will be due on Tuesdays of the week announced. For the grader's benefit, late solutions will be penalized: 75% credit for solutions turned in before the following Tuesday; no credit after that time. You may miss one homework set with no penalty.

Term Paper

Each student is expected to complete a term paper on a topic that he/she has investigated in more depth than would be possible as a topic in the course. A list of suggested topics will be given out, but each person can choose his or her own topic. Be sure to discuss the topic of your paper with Prof. Martin before proceeding! The primary objective of the term paper should be to describe a physics issue in such a way that other students at this level can benefit by reading the paper. It may be a summary of what is known about a research topic from the literature; it may describe a problem and its solution or partial solution; or it may describe a computational method for solving a problem. Appropriate references to the literature should be included just as in a paper to be published. The term papers should be typed in the style of a paper using REVTEX, which is the accepted format for Physical Review papers and is widely available. The final version should include figures and be in a single pdf or postscript file. The staff will help you with aspects of REVTEX. The term papers will be collected in a volume, reproduced, distributed to all students, and published electronically on the class web pages

Exams

The will be a mid-term and a final exam. The nature of the exams will be discussed well in advance of the exams.

Grades

The grades will be determined approximately as follows: problem sets (30%), term paper (25%), mid-term exam (15%), and final exam (30%).

Course Materials

The material covered in the lectures will follow a set of Lecture Notes, which will be made available. The syllabus for the course and short summaries of the notes for each lecture, with the primary references, will be posted on the web pages, and will be passed out at the lectures. Some extensive notes will be posted on the web pages in pdf.

Texts and Other Materials

There is no one textbook that I consider covering the material for this course. I have chosen is Advanced Solid State Physics by Philip Phillips (Westview Press; 1st edition, 2002, Paperback: 416 pages, ISBN: 0813340144). This book is a relatively new one that has a more modern approach than other books that are also very good. In particular, I will use Mahan, Many Particle Physics, for some of my preparation because it is a good text for many-body methods with many details especially for the various Green’s functions that are important in advanced solid state physics. I regard other texts as very good; I will use them, but they are "old-fashioned" and not appropriate as the main texts: Elementary Excitations in Solids by Pines, which is a good introduction to the physics of quasiparticles, and Abrikosov, Gorkov and Dzaloshinki, which is a real classic now available in low-cost Dover paperback. For superconductivity the new edition of the book by Tinkham is very good. Finally, a text like Solid State Physics, by Ashcroft and Mermin, is needed. I recommend this one because I consider it the best background text for 560 level material with some of the 561 level material. (If you have another text, e.g., Kittel, Introduction to Solid State Physics, or Ziman, Principles in the Theory of Solids, then use that instead.) Below I also list the books I have found most useful in preparing the detailed contents of my lectures and other useful books. All of these books are on reserve in the library.

A review article (Rev. Mod. Phys. 70, 1039 – 1263 (1998)) on "Metal-Insulator Transitions and Correlated Metals in d-Electron Systems" by M. Imada, A. Fujimori, and Y. Tokura, will be used in the class for the portion on strongly-correlated electrons in the d and f systems. This review covers both theory and experiment, and it will certainly not be possible to cover it in detail, which would require an entire course. We will attempt to cover this in enough detail that students can choose topics for further study for a term paper.

Texts and Reference Books

Required Text

Phillips, P.

Advanced Solid State Physics

Recommended Texts

*	Mahan, G.	Many-Particle Physics, 2nd Ed
*	Pines, D.	Elementary Excitations in Solids (An index is available from Prof. Martin)
*	Tinkham, M.	Intro. to Superconductivity, 2^nd Edition (Dover Paperback)
*	Abrikosov, A., et.al.	Quant. Field Th. Methods in Statistical Phys. (Dover Paperback)
*	Ashcroft & Mermin	Solid State Physics (or a similar text)

Other Books on Reserve in the Physics Library

	Anderson, P. W.	Concepts in Solids
	Anderson, P. W.	Basic Notions of Condensed Matter Physics
*	Coleman, P.	Notes for book in progress posted at Rutgers University	*
*	de Gennes, P.	Superconductivity of Metals and Alloys
*	Doniach, S. & Sondheimer	Greens Functions for Solid State Physicists
	Elliott, R.	An Introduction to Solid State Physics
*	Fetter, A. & Walecka	Quantum Theory of Many-Particle Systems
	Feynman, R. P.	Statistical Mechanics, A Set of Lectures
*	Fradkin, E.	Field Theories of Condensed Matter Systems
	Gross, E. K. U.	Many-Particle Theory
	Harrison, W.	Solid State Theory
	Hedin, L. & Lundquist, S.	Solid State Physics, Vol. 23, p. 1.
	Ibach, H. & Luth, H.	Solid State Physics, An Intro. to Theory and Exper..
*	Imada, M., et al	preprint of review Rev. Mod. Phys.
		"Metal-Insulator Transitions and Correlated Metals in d-Electron Systems"
	Jones & March	Theoretical Solid State Physics
	Kadanoff, L. & Baym, G.	Quantum Statistical Mechanics
	Kittel, C.	Introduction to Solid State Physics
	Kittel, C.	Thermal Physics
	Kittel, C.	Quantum Theory of Solids
	Madelung O.	Introduction to Solid State Theory
*	Martin, P. C.	Measurements and Correlation Functions
*	Martin, R. M.	Electronic Styructure: Basic Theory and methods
*	Negele, J. W. & H. Orland	Quantum Many-Particle Systems
*	Pines, D. & P. Nozieres	Quantum Liquids Vols 1 & 2
	Reif, F.	Fundamentals of Statistical and Thermal Physics
	Rickayzen, G.	Theory of Superconductivity
	Schrieffer, R.	Superconductivity
	Seitz, F.	Modern Theory of Solids
	Thouless, D	The Quantum Mechanics of Many-body Systems
	Weinreich, G.	Solids: Elementary Theory for Advanced Students
	Zagoskin, A. M.	Quantum Theory of Many-Body Systems
	Ziman, J. M.	Principles of the Theory of Solids
*	Ziman, J. M.	Elements of Advanced Quantum Theory

* Books I will use in preparing course

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