syllabus - David A. Rabson

Physics PHZ-6426, fall semester 2006SOLID-STATE PHYSICSPART IIInterviewing Professor Hans A. Bethe (1906{2005) in 2003, David Mermin noted howmuch of the contentof his book with Neil Ashcroft was already present in Bethe and Sommerfeld's 1933 review of the theory ofsolids. It is a goal of this course to introduce some physics that was discovered in the students' lifetimes(or at least in those of their parents). Since the quantity of solid-state physics discovered since 1933would (and does) ll a medium-sized library, the challenge for the instructor of Part II of the one-yearsequence is to select a subset of that library. With input from students, I have decided to survey threetopics, any one of which could easily ll a semester course by itself:1. Mesoscopic Transport2. Magnetism in Matter3. SuperconductivityOne cannot imagine anyone calling herself an experimental or theoretical solid-state physicist in theyear 2006 who has not studied something of the peculiar electrical properties of structures fabricatedin nanometer-scale geometries, of magnetic materials, and of the Bardeen-Cooper-Schrieer theory ofsuperconductivity. These frame the course. A great deal has necessarily been left out. Because the focusis on ideas that will be as useful to experimenters as to theorists, we shall not touch on the standardtoolkits of theoretical physics, such as diagrammatic perturbation theory and computational methods inelectronic structure.Dr. David A. RabsonPhysics and Mathematics Building 304Telephone: 974-1207Telephone facsimile: 974-5813e-mail: davidra@ewald.cas.usf.eduWeb: http://ewald.cas.usf.eduMEETING TIMES: Tuesdays and Thursdays 14:00{15:15 in room 130, Mathematics-Physics building(PHY). Ocial OFFICE HOURS will be announced; I am also usually available during the day,evenings, and weekends. You may give away notes for free but may not sell them or tapes.prerequisitesPart II builds on the core topics treated in PHZ 5405, \Solid-State Physics I," a coursegenerally taught at the level of Ashcroft and Mermin or Kittel ISSP (see bibliographybelow). Alternatively, EEL 5382, \The Physical Basis of Microelectronics," may serve asan introduction to this material to a student who also has a good grasp of thermodynamics,electromagnetics, and quantum mechanics. In particular, we shall assume familiaritywith Fermi surfaces, band structure, elementary crystallography, semiclassical transport,and wave mechanics.Course structure and evaluationTests. While the three parts of the course have some thematic overlap|coexistence of magnetism andsuperconductivity, for example, is a hot topic|they are far more independent than usual for a course likethis. I've decided therefore to have sit-down (rather than take-home) examinations after each of the threeparts. The nal examination will be the third of these, covering only the segment on superconductivity.I shall attempt to make the tests easy and short (35 minutes each, 9/28, 11/2, and 12/12 [the last at1:00 PM]).Homework and Oral Presentations. Homework will be assigned weekly or biweekly and will havetwo parts. Two of our primary textbooks solve substantially all of the problems set at the ends ofchapters; I will assign a few of these each week in the rst two parts of the course and expect every1

student to prepare each problem, lling in missing details. I will call students randomly to the chalkboard to present their solutions and answer questions from the audience. Try to keep presentations to10 minutes per problem. These presentations will form part of the grade. Since you won't know whenyou'll be called, you should be ready at each lecture to present anyof the problems most recently due.If you cannot be in class, you need to let me know in advance. Once in a while, something might comeup that prevents you from being able to do a good job of preparing your problems; rather than missingclass, just call or send me an e-mail before lecture saying that you don't wish to be called. While I don'tmind if you do this one or two times, don't abuse the privilege. The second part of homework will betraditional problems to turn in; I will correct the assignments and make comments. The number (andprobably the complexity) of such problems will be smaller than in Solid-State I: the closer we get tocurrent research, the harder it is to make up problems that aren't current research.Critical Review Paper. The last item evaluated will be a critical review of some topic in one of thecourse's three broad areas that remains, as of 2006, controversial. An example that would have appliedthrough the mid-1990s would be the order parameter, s- or d-wave, of high-temperature superconductors.You need to identify a scientic controversy, that is, a question on which broad consensus hasnot been reached as to the validity, applicability, or theoretical interpretation of some experiment orexperimentally-accessible question. Then nd and understand all the relevant papers (from at least twodierent groups). Your paper will review the experimental and theoretical arguments on all sides of theissue and discuss the reasons for the disagreements. Iwould also like you to propose possible experimentsor calculations that might resolve the issue and, if appropriate, you may speculate on why these havenot yet been performed.You might wish to spend a few hours in the library with journals suchasPhysical Review B just to identifya suitable question. Be careful of picking too broad a topic: a review of proposed mechanisms of hightemperaturesuperconductivity would run to hundreds of pages. However, a small, well-dened aspectof this question could be appropriate. Please limit the length of your paper to seven pages, excludingbibliography but including graphs, gures, and tables, and, as far as practical, follow the typography andbibliographic format of an article in Reviews of Modern Physics. In particular, to maximize readabilityand discourage circumvention of the seven-page limit, I ask you not to exceed the type density (averagenumber of characters per centimeter horizontally and number of lines per centimeter vertically) of theprinted version of that journal. You may nd it convenient to use the Revtex macro package availablefrom the American Physical Society.The topic should pertain to one of the three parts of this course and not parallel your own researchor your advisor's. Thus, if you are working in nanoscale transport, you may write about magnetismor superconductivity; if you are working in magnetism, you may write about mesoscopic physics orsuperconductivity. Before the rst of November, please make an appointment to talk with me aboutyour proposed topic. I am not looking just for a summary of published research, on the order of \A didthis, and B did that," although that will necessarily form a part of the paper. Rather, I am interestedin a critical synthesis seeking a deeper understanding of the reasons behind the controversy.Your paper should observe scholarly conventions on citations. Read and understand the sectionin the Graduate School's Policies and Procedures handbook on scholarly misconduct andplagiarism. When turning in any assignment, including homework and the review paper in this class, astudent implicitly certies that the work, the ideas, and the wording are his or her own except as otherworks have been cited clearly. Briey, not citing a work from which one has borrowed ideas is a formof dishonesty; copying phrases verbatim without setting them o typographically and citing the sourceis plagiarism. \Padding" a bibliography with papers one has not read is also considered academicallydishonest. 1 Note that the University Graduate Committee approved a new policy on 17 October 2005under which plagiarism will, without exception, result in dismissal from the university and ineligibilityto re-apply to any graduate program at USF in the future.1 Iwould not go so far as to require complete and thorough understanding of all aspects of all paperscited, but you need at least to be able to show what in the cited source makes it relevant.2

Part I: Mesoscopic Transport, 8/30{9/29primarytextbookSupriyo Datta, Electronic Transport in Mesoscopic Systems, Cambridge, 1996, $44 (Amazon).Chapters 1, 2, and 4 will provide most of the material for the rst third of thecourse. For reviews, see Contemp. Phys. 39, 401 (1996) and Phys. Today, May 1996,p.70.In Solid-State I, we studied the properties of periodic, bulk matter. Samples were always innite, and,with the exception of the p-n junction, we had nothing to say about interfaces. Starting in the 1980s,experimental techniques such as improved lithography and molecular-beam epitaxy enabled scientiststo create articial structures with one or more dimensions on the nanometer scale. Such a structure,containing many more degrees of freedom than a single atom, may not be treated with atomic theory,but because one dimension or more is small compared to a mean free path or other scattering length,neither is the simple bulk theory applicable. This is the regime of mesoscopic physics, the interfacebetween quantum and classical behavior. As two examples of the strange things that can happen, we'lllook at the resistances of mesoscopic wires in series (they don't add) and at the quantum Hall eects.Yoseph Imry's Introduction to Mesoscopic Physics, 2nd ed., is also on reserve in the library. It is bothmore advanced and sketchier than Datta's book and probably a bit closer to current research in its focus.Advanced Solid-State Physics by Philip Phillips (probably the best dressed physicist at the APS Marchmeetings) is a really nice book and will be useful when we get to the quantum Hall eects. I might usethis book (alone) as a primary textbook for Solid State II in some future year. The focus is somewhatmore theoretical than in this course. (On reserve.)The book on the Quantum Hall Eect edited by Prange and Girvin is a standard reference.Part II: Magnetism in Matter, 10/4{11/3primarytextbookStephen Blundell, Magnetism in Condensed Matter, Oxford, 2001, $50 (Amazon). Thisis primarily an undergraduate textbook, and it does a good job providing the readerwith the vocabulary she needs to pursue research in magnetic materials. I expect to getthrough most of the book. For a review, see Contemp. Phys. 44, 377 (2003).Two of the lies taught in elementary textbooks are that magnetism is part of classical electrodynamics andthat there are three types: ferromagnetism, paramagnetism, and diamagnetism. Bohr and van Leeuwenindependently showed that all of these types of magnetic ordering are impossible in classical mechanics atany non-zero temperature. Further, the magnetic zoo, far from being conned to three animals, is worthyof a Dr. Seuss book: we shall try to touch on antiferromagnetism, ferrimagnetism, metamagnetism,superparamagnetism, speromagnetism, sperimagnetism, mictomagetism, and helimagnetism, as well asthe disordered magnetic state of a spin glass.In addition to the Blundell text, I'd like everyone to read the rst, historical, chapter from the secondprinting of Daniel Mattis's Theory of Magnetism Part I. I shall make this available to students as weapproach the second part of the course. The textbook for Solid-State I, Ashcroft and Mermin Solid-StatePhysics hasachapter on magnetism as well as one on superconductivity.Part III: Superconductivity, 11/8{12/8primarytextbookMichael Tinkham, Introduction to Superconductivity, 2nd ed., Dover, 2004 (reprint of1996 McGraw-Hill second edition), $20 (Amazon). This is the most theoretical of thethree main textbooks. Naturally, itwas written by an experimenter (who is also a rstclasstheorist). For a review, see Phys. Today, Oct. 1996, p.74.Superconductivity belies the fairy tale supposing that quantum is small, classical is big. Here is a purelyquantum-mechanical phenomenon, marked by truly zero electrical resistance|currents have persistedin rings for years without any measurable degradation|in macroscopic samples. After reviewing phenomenologyand the London theory, we'll study the Bardeen-Cooper-Schrieer theory, which has to beone of the most subtle and surprising results in all physics.Bob Schrieer's Theory of Superconductivity will also be on reserve in the library.3