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Physics PHZ-6426, Fall Semester 2010 SOLID-STATE PHYSICS PART II

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Physics PHZ-6426, Fall Semester 2010 SOLID-STATE PHYSICS PART II Physics PHZ-6426, fall semester 2010 SOLID-STATE PHYSICS PART II Interviewing Professor Hans A. Bethe (1906–2005) in 2003, David Mermin noted how much of the content of his book with Neil Ashcroft was already present in Bethe and Sommerfeld’s 1933 review of the theory of solids. This, presumably, was the era of most students’ great grandparents. 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 1933 would fill a medium-sized library, the challenge for the instructor of Part II of the one-year sequence is to select a subset of that library. With input from students, I have decided to survey three topics, any one of which could easily fill a semester course by itself: 1. Magnetism in Matter 2. Superconductivity 3. Mesoscopic Transport One cannot imagine anyone calling herself an experimental or theoretical solid-state physicist in the year 2010 who has not studied something of the peculiar electrical properties of structures fabricated in nanometer-scale geometries, of magnetic materials, and of the Bardeen-Cooper- Schrieffer theory of superconductivity. These frame the course. A great deal has necessarily been left out. Because the focus is on ideas that will be as useful to experimenters as to theorists, we will not study in any depth the standard toolkits of theoretical physics, such as diagrammatic perturbation theory and computational methods in electronic structure. Dr. David A. Rabson Physics and Mathematics Building 304 Telephone: 974-1207 Telephone facsimile: 974-5813 e-mail: [email protected] Web: http://ewald.cas.usf.edu MEETING TIMES: Wednesdays and Fridays, 12:55–14:10, in room 130, Mathematics-Physics building (PHY). Official OFFICE HOURS will be announced; I am also usually available during the day, evenings, and weekends. prerequisites Part II builds on the core topics treated in PHZ 5405, “Solid-State Physics I,” a course generally taught at the level of Ashcroft and Mermin or Kittel ISSP. In particular, we shall assume familiarity with Fermi surfaces, band structure, elementary crystallography, semiclassical transport, and wave mechanics. Course structure and evaluation Tests. While the three parts of the course have some thematic overlap—coexistence of magnetism and superconductivity, for example, is a hot topic—they are closer to independent than usual for a course like this. I’ve decided therefore to have sit-down (rather than take-home) examinations after each of the three parts. The final examination will be the third of these, covering only the segment on quantum transport. I shall attempt to make the tests easy and short (40 minutes each, 9/24, 10/29, and 12/10 [the last at 12:30 PM]). 1 Homework and Oral Presentations. Homework will be assigned weekly or biweekly and will have two parts. In the first part, students will rotate giving short presentations based on worked problems or sections in the textbooks. Try to keep presentations to 10 minutes per problem. These presentations, and participation in the form of asking questions, will form part of the grade. In past years, I’ve called on people randomly as a way of making sure everyone’s prepared each problem. Students didn’t like this, so I’ll let people reserve presentation slots. The second part of homework will be traditional problems to turn in; I will correct the assignments and make comments. The number (and probably the complexity) of such problems will be smaller than in Solid-State I: the closer we get to current research, the harder it is to make up problems that aren’t current research. When turning in any assignment, including homework, a student implicitly certifies that the work, the ideas, and the wording are his or her own except as other works have been cited clearly. Briefly, not citing a work from which one has borrowed ideas is a form of dishonesty; copying phrases verbatim without setting them off typographically and citing the source is plagiarism. Since good communication is essential to science and to your professional development, grammar, organization, and style count. Students are encouraged to discuss homework, but cooperation must not include copying or plagiarism. You may look things up in books and journals in the library, but looking at previous years’ solutions, solutions on the Web, or a manual of answers is cheating and will result in expulsion from the university under a policy of the USF Graduate Council. You need to cite any outside sources (i.e., other than the required textbooks) you consulted on the homework: as examples, before a derivation (which you may follow but not copy verbatim) you might write “this derivation fills in the missing details in section 10.9 of Jackson, third edition,” or before a difficult integral, “Mary showed me this integral in Gradsteyn and Ryzhik, (3.456).” Part I: Magnetism in Matter, 8/25–9/24 primary Stephen Blundell, Magnetism in Condensed Matter, Oxford, 2001. This is primar- textbook ily an undergraduate textbook, and it does a good job providing the reader with the vocabulary she needs to pursue research in magnetic materials. I expect to get through 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 electrody- namics and that there are three types: ferromagnetism, paramagnetism, and diamagnetism. Bohr and van Leeuwen independently showed that all of these types of magnetic ordering are impossible in classical mechanics at any non-zero temperature. Further, the magnetic zoo, far from being confined to three animals, is worthy of a Dr. Seuss book: we shall try to touch on antiferromag- netism, ferrimagnetism, metamagnetism, superparamagnetism, speromagnetism, sperimagnetism, mictomagetism, and helimagnetism, as well as the disordered magnetic state of a spin glass. In addition to the Blundell text, I’d like everyone to read the first, historical, chapter from the second printing of Daniel Mattis’s Theory of Magnetism Part I. The textbook for Solid-State I, Ashcroft and Mermin’s Solid-State Physics, has a chapter on magnetism as well as one on superconductivity. Part II: Superconductivity, 9/29–10/29 primary Michael Tinkham, Introduction to Superconductivity, 2nd ed., Dover, 2004 (reprint textbook of 1996 McGraw-Hill second edition). This is a theoretical textbook. Naturally, it was written by an experimenter (who is also a first-class theorist). For a review, see Phys. Today, Oct. 1996, p.74. 2 Superconductivity belies the fairy tale supposing that quantum is small, classical is big. Here is a purely quantum-mechanical phenomenon, marked by truly zero electrical resistance—currents have persisted in rings for years without any measurable degradation—in macroscopic samples. After reviewing phenomenology and the London theory, we’ll study the Bardeen-Cooper-Schrieffer theory, which has to be one of the most subtle and surprising results in all physics. Pierre-Gilles de Gennes’s Superconductivity of Metals and Alloys will also be on reserve in the library. Part III: Mesoscopic Transport, 11/3–12/3 primary Nazarov and Blanter, Quantum Transport, Cambridge, 2009. We’ll treat selected textbook topics from chapters 1–4. See the review in Physics Today, May 2010, pp. 46–7. In Solid-State I, we studied the properties of periodic, bulk matter. Samples were always infinite, 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 scientists to create artificial structures with one or more dimensions on the nanometer scale. Such a structure, containing many more degrees of freedom than a single atom, is too complex to solve 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 interface between quantum and classical behavior. As two examples of the strange things that can happen, we’ll look at the resistances of mesoscopic wires in series (they don’t add) and at the quantum Hall effects. In past years, we used Supriyo Datta’s Electronic Transport in Mesoscopic Physics, and this is on reserve in the library along with Yoseph Imry’s Introduction to Mesoscopic Physics, 2nd ed. The latter is both more 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 March meetings) is a really nice book and will be useful when we get to the quantum Hall effects. I might use this book (alone) as a primary textbook for Solid State II in some future year. The focus is somewhat more theoretical than in this course. The book on the Quantum Hall Effect edited by Prange and Girvin (2nd ed.) is a standard reference. I’ll ask you to read the introduction, a reprint of which is available at Pro Copy (next to Publix on Fowler) for $13. 3.
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