Syllabus

This quarter we will concentrate on physics relevant to important semiconductors.

• Linear reponse, Drude theory of conductivity, relaxation time, resistivity tensor in a magnetic field

• Hall effect, Hall bars, 2D electron gas, quantum Hall effect, conductance quantization

• Thermal conductivity, Wiedemann-Franz law, Sommerfeld theory for metals,

• Boltzmann equation, nonequilibrium distribution function, Fermi surface properties

• Lattices, unit cells, symmetry

• Scattering and Bragg's law; reciprocal lattices

• Bloch theorem and Brillouin zone for lattice vibrations; phonons

• Band theory for electrons

• Effective mass; electrons and holes; band diagrams for semiconductors

• Liquid crystals (2 lectures by David Allender)

• Doping, statistics of semiconductors, p-n junctions

• Interfaces, work function, surface states

• Transistors

• Light emitting diodes and semiconductor lasers

• Photoluminescence, excitons

• Photovoltaic effects

• Thermoelectric effects

Prerequisites: You should ideally have had some previous exposure to concepts in solid state/condensed matter, such as through an undergraduate level course. More importantly though, you should have undergraduate quantum mechanics, electromagnetism and statistical mechanics.

Grading: Reading suggestions and problems will be given for self-study. There will be no exams, and all completing the course satisfactorily will receive 4.0.

Meeting times: MW 1.30-2.50 pm. Location: Physics B109

The syllabus for 2008 was a more general two-quarter introduction to condensed matter

Physics 567 and 568 aim to introduce the most important concepts of modern condensed matter physics at the beginning graduate level.

567 Condensed Matter I - General principles, structure, scattering and vibrational properties

• Phases of matter characterized by symmetry and order.  Phase transitions.  Symmetry breaking and its consequences.
• Cohesion.  Thermodynamics of condensation.  Competition between kinetic, potential energy and entropy.  Born-Oppenheimer approximation.  Van der Waals interaction.  Ionic solids and Madelung constant.  Chemical bonding (Heitler-London model).  Exchange.  Lennard Jones potential.  Metallic bonding, LCAO.
• Quasi-elastic scattering of X-rays, neutrons, electrons. Structure factor and density-density correlation functions.  Structure in liquids.
• Crystal lattices, reciprocal lattice, translation and point groups.
• 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.

568  Condensed Matter II - Electronic properties

• 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
• Tight binding model. Hubbard model
• Band structure calculations and examples. Graphene
• Bloch electron dynamics in E and B fields. Semiclassical approximation
• Holes.  Semiconductors. Cyclotron motion, Landau levels. Skin effect

569  Condensed Matter III - Transport and response (planned but not yet implemented)

• Drude model. Magnetoresistance and Hall effects
• Boltzmann equation. Relaxation time approximation. Electrical and thermal conductivity. Impurity scattering
• Linear response. Einstein and Onsager relations. Thermoelectric coefficients
• Thomas-Fermi Screening. Lindhard function. Friedel oscillations and sum rule
• Dielectric response function; Kramers-Kronig relation etc.
• Plasmons in 3D and confined geometry
• Electron-phonon coupling. Peierls instability. Polarons
• Basics of magnetism

Other possible topics

• 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.
• 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

Books

Our guiding texts this quarter will be

Condensed Matter Physics [2000] by M.P. Marder (Wiley; make sure you get the corrected printing from 2004). This book is is an up-to-date, rather broad coverage of CM physics. Some important topics are only sketched, but a remarkably large number are done in depth, with more sophisticated calculations than presented in the other texts. 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.

Advanced Condensed Matter Physics [2009] by Leonard M. Sander. A brand new book at a similar level of sophistication to Marder but with far less detail but clearer notation and explanations. It is sketchy and needs to be used in conjunction with other bigger books, such as Marder.

Solid State Physics [1976] by N.W. Ashcroft and N.D. Mermin. The clearest, wordy explanations at advanced undergrad level; not as sophisticated or modern as the above books but authoritative.

Principles of the Theory of Solids [1979] by J.M. Ziman. Slick and concise grad level book focused on crystalline solids, packed with insights and self-contained, but with no problems.

Also useful:

Principles of Condensed Matter Physics [2000] by P.M. Chaikin and T.C. Lubensky.� Advanced and up-to-date text with an unusual emphasis on soft condensed matter. Complementary to Marder. Very light on 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. Supposed to be the authority 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. Quirky, and addressed to the professional. The use of the word 'basic' in the title is highly 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 undigestible book. Earliest editions were better.

Some other 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 ambitious compendium; falls in the gap between general and authoritative.

Condensed matter resources on the web

Marder's web site
Statistical Mechanics: Entropy, Order Parameters and Complexity by Jason Sethna
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
Gil Refael (CalTech) - Statistical Mechanics and Critical Phenomena