Meeting times: Wednesday and Friday, 1.30-2.50 pm. Location: officially A114, but we should find somewhere cosier.

Course desription: This course, 567B, will actually be the SECOND of a proposed a three-quarter graduate sequence which is under development.  The first quarter, 567A, was taught last year.  Note that at present, Phys 568 is not part of this sequence but is a special topics class.

Prerequisites: Students should ideally have had some previous exposure to concepts in solid state/condensed matter, such as through an undergraduate level course, and through taking 567A. Undergraduate level quantum mechanics, electromagnetism and statistical mechanics will naturally be assumed.

Grading: there will be weekly problem assignments and reading suggestions. No exams. During this development period, everyone completing the course satisfactorily will receive a 4.0 grade.

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Syllabus

567B (tentative and way overambitious)

• Review of 567A syllabus
• Bloch electron dynamics in E and B fields.  Holes.  Cyclotron motion, Landau levels.  Skin effect.  Hall effect.
• Boltzmann equation.  (Problems by Adam)  Relaxation time approximation.  Electrical and thermal conductivity.   Impurity scattering. Fermi liquid.
• Linear vs nonlinear response.  Einstein and Onsager relations. Thermoelectric coefficients.
• Hartree-Fock approximation.  Thomas-Fermi Screening. Lindhard function.  Friedel oscillations.
• Dielectric response function; Kramers-Kronig relation
• Plasmons in 3D, on surfaces, and in nanoparticles.
• Electron-phonon coupling. Peierls instability. Polarons.
• Diamagnetism. De Haas van Alphen effect. Spin-orbit coupling.
• Aspects of magnetism: Ferromagnetism; mean-field theory, Curie-Weiss, antiferromagnetism, Bloch walls.  Ginzburg-Landau theory.
• Bloch equations, spin decoherence, superparamagnetism, g-factors, magnetic resonance.  Tunneling, GMR.
• Semiconductors, impurities, band diagrams, p-n junctions.  Excitons.
• Interfaces.  Surface states.  Surface reconstruction.  Work function.  Thermopower.  Kelvin probe.
• Landauer formula. Point contacts and conductance quantization. Resonant tunneling.

This is what we did in 567A in Winter 2007:

• Cohesion. Lennard Jones potential, noble gas solids, Madelung constant. Bonding (Heitler-London, LCAO). Born-Oppenheimer approximation.
• Symmetry, symmetry breaking, and consequences. Phases of matter characterized by symmetry and order. Density-density correlation function and structure factor.
• Crystal lattices.  Translation and point groups.
• Elastic scattering of X-rays, neutrons, electrons. Structure factor and reciprocal lattice.
• Bloch theorem. Brillouin zone. Density of states.
• Lattice vibrations. Harmonic approximation, dynamical matrix, classification of modes.
• Phonons. Heat capacity, density of modes, Einstein and Debye models.
• Anharmonic effects: phonon-phonon scattering processes; umklapp; temperature dependence of thermal conductivity; thermal expansion.
• Inelastic scattering spectroscopy: neutrons, Raman and X-ray spectroscopy; Debye-Waller factor.
• Free electrons, Sommerfeld expansion, statistics, second quantization. Heat capacity of electron gas. Pauli susceptibility.
• Bloch theorem for electrons. Band structure and group theory.
• Nearly free electron model.  Metals and insulators.  Drude model.
• Tight binding model.  Hubbard and Anderson models.
• Band structure calculations and examples.

Topics left over ...

• Pseudopotentials.  Density functional theory.  Photoemission spectroscopy
• Coulomb blockade. Semiconductor quantum dots. Shell filling and exchange
• Dephasing mechanisms. Inelastic scattering of electrons
• Impurities. Quantum interference. Mesoscopic effects, universal fluctuations. Strong and weak localization; scaling. Anderson, Thouless and Mott criteria. Hopping conduction
• Friedel sum rule. Lindhard function. RKKY interaction, superexchange
• Fluctuation-dissipation theorem.  One-particle Green’s function. Quantum Kubo formula. Tunneling
• Ising and Heisenberg models
• Quantum Hall effect
• Fractional QHE
• Berry phase and curvature
• Stoner model, magnons, spin as bosons, superparamagnetism, spin density waves
• Polymers
• Liquid crystals
• Many-body effects in tunneling. Orthogonality catastrophe. Action for tunneling. TDOS. X-ray edge and Fermi edge singularity. Interaction corrections to conductivity
• All of superconductivity, BCS, order parameter, junctions, SQUIDs, qubits
• Optical properties of semiconductors. Absorption and photoluminescence. Excitonic stuff.  Frank-Condon. LEDs and Laser diodes
• Alloys
• Quasicrystals
• Ginzburg-Landau theory
• Superfluidity, vortices
• RG and critical exponents
• Bogoliubov transformation
• Bose-Einstein condensates
• Transition metal oxides
• Quantum phase transitions
• Many-body Green’s functions
• Mott-Hubbard transition
• Kondo effect, heavy fermions, Kondo insulators
• Luttinger liquid
• Elasticity
• Buckling, defects and cracks
• Hydrodynamics
• Plasmas and electrolytes
• Nonlinear Schoedinger equation?
• Detailes of density functional and other calculational schemes
• Glasses, amorphous metals, spin glasses
• Mixtures and foams
•  X-ray edge fine structure analysis
• Conformal field theory
• Interfacial growth, ripening, transport, KdV equation Diffusion limited aggregation,
• Sandpiles, jamming

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Books

Our guiding texts will be

Condensed Matter Physics [2000] by M.P. Marder (Wiley; make sure you get the corrected printing from 2004). The great thing about this book is that it is an up-to-date, rather broad coverage of CM physics. Some important topics are only sketched, others are done in depth. The book has a relatively conventional coverage of crystalline materials and electronic properties. The author has a web site for the book and a complete set of nice lecture slides is available as pdf files.

Solid State Physics [1976] by N.W. Ashcroft and N.D. Mermin.  The clearest, wordy explanations at advanced undergrad level.

Principles of the Theory of Solids [1979] by J.M. Ziman.. Very well written and incredibly concise grad level book.

Also recommended:

Principles of Condensed Matter Physics [2000] by P.M. Chaikin and T.C. Lubensky. Another advanced and up-to-date text with an unusual emphasis on soft condensed matter. Complementary to Marder.  Almost no discussion of electronic properties.

Solid State Physics [1995] by J.R. Hook and H.E. Hall
Undergraduate level book, full of insights, but somewhat unorthodox in the development of the subject. Excellent contact with experiments (written, unlike any of the other books, by experimentalists.) Nonstandard approaches to several issues may upset undergraduates but can be informative for graduate students and people like me who are looking to understand things better.

A Quantum Approach to Condensed Matter Physics [2002] by P. Taylor and O. Heinonen.
Nice intro to second quantization and diagrams. Rather unorthodox approach; skimpy on details of some standard CM material and little contact with experiments. This book goes as far into field-theory as a non-field-theorist could want.

Fundamentals of the Theory of Metals [1988] by A.A. Abrikosov. Absolutely authoritative on metals but out of print and very hard to get hold of.

Basic Notions of Condensed Matter Physics [effectively 1973] by P.W. Anderson. Very hard to read but full of deep insights. The use of the word 'basic' in the title is misleading.

Introduction to Solid State Physics [8th Edtion, 2004] by C. Kittel.  Generations of students have been put off condensed matter physics by this encyclopaedic but horribly written book.

Some other useful newer books:

Many-Body Quantum Theory in Condensed Matter Physics [2004] by H. Bruus and K. Flensberg. Good for learning to do many body calculations from scratch, if that's what you're into.

Introduction to Condensed Matter Physics [2005] by F. Duan and J. Guojun. First volume of an overambitious compendium.

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Condensed matter resources on the web

Marder's web site

MIT Theory of Solids

Physics of Mesoscopic Systems  Lecture notes from Boulder school, July 4-29, 2005

Ben Simons (Cambridge) - Quantum Condensed Matter Physics and Quantum Condensed Matter Field Theory

Piet Brouwer (Cornell) - problem sets

Yuri Galperin (Oslo) - Introduction to Modern Solid State Physics

Chetan Nayak (UCLA)

Piers Coleman (Rutgers) - Monogram on Many Body Physics