Introduction into Condensed Matter Physics 133

Spring 2018

Tuesday & Thursday, 2:00pm-3:20pm
PSCB 220

Introduction

Topics to be covered

• Crystal structures [Kittel, Ch. 1, 2],
  • Periodic structures, idea of crystals
  • Bravais lattices, unit cells
  • Point group symmetries
  • 2D, 3D Bravais lattices
  • lattices with basis, Lecture 1 and 2
  • Inverse lattice, vectors, symmetries
  • Bragg planes, indices
  • Scattering problem, Bragg's law Lecture 3 and 4
  • X-rays, electrons, neutrons, physical restrictions
  • surfaces, experiments (LEED, STM, etc.)
  • Correlation functions, structure factor
  • Long-range order, order parameter
  • quasicrystals
  • some extra stuff (bonding, elasticity etc.) overview
• Phonons as quanta [Kittel, Ch. 4, 5] Lecture 5 and 6
  • Bravais/non-Bravais, 1D examples
  • longitudinal, transverse, optical modes
  • equation of motion, translational invariance, Fourier transform
  • coupled harmonic oscillators --> independent harmonic oscillators
  • universality, emergence of excitations
  • Normal modes, second quantization, number representation
  • phonon distribution function, chemical potential
  • specific heat, Debye approximation, limiting cases, universality
  • thermal conductivity, mean-free path, Umklapp skattering
  • Density of states, 1D, 2D, 3D; van Hove singularities
  • (*) Crystalline order in one- and two-dimensions
• Electronic properties of solids, bands [Kittel, Ch. 6, 7, and 9]
  • Basic Hamiltonian, adiabatic approximation
  • non-interacting (free) Fermi-gas, Lecture 7 and 8
  • Ground state properties, useful quantities (kF, rs, EF)
  • Density of states
  • Specific heat, T-dependence of mu, Sommerfield constant
  • Translational invariance, waves in crystals, Bloch's theorem, Lecture 9, 10, 11, and 12
  • Folding to the Brillouin zone
  • "nearly-free" electrons, Schroedinger E. in momentum space
  • Perturbation theory in momentum space
  • Role of Bragg scattering near BZ boundaries, band formation
  • van Hove singularities, Kronig-Penney model
  • Folding of the Fermi surfaces, Harrison construction,
    Alternative slides
  • Tight-binding, idea, justification, bands
  • hopping integrals, Hamiltonian, effective mass,
    Extra material on tight-binding
  • Brief overview of the periodic table
    
  • role of e-e interaction, Mott effect, idea of DFT
    
• Elements of the theory of semiconductors [Kittel, Ch. 8 and 17]
  
  • semiconductors, band gap
    
  • direct and indirect gaps, optical properties
    
  • intrinsic carrier concentration
    
  • holes, effective mass
    
  • doping, donors, acceptors
    Lectures 14 and 15
  • thermal ionizatopn, p- n-types
    
  • p-n junction,diode, transistor; applications
    
  • solar cells, photovoltaic effect
    
• Superconductivity [Kittel, Ch. 10]
  • superconductivity, survey, materials, energy scales
    
  • Meissner effect, persistent currents
  • Josephson effect, SQUID
  • Type I, Type II, vortices
  • specific heat, gap, tunneling
  • energy gap, pairing, effect of field, isotope effect
  • Ginsburg-Landau
  • BCS theory
  • Ch. 3-6 from a short book on Superconductivity and Superfluidity by Annett
  Lecture that follows Kittel
  Less formal lecture
  A lecture on BCS and Josephson

Recommended Book

• Charles Kittel, Introduction to Solid State Physics, 8th Edition

A note about this text: Kittel's textbook is good, but not to everyone's liking.
It is, therefore, recommended, but will not be required.
There is plenty of other books as well as excellent on-line sources
such as this one.
Here is a set of very nice lecture notes based on a different book.
It has a significant overlap with my lectures.

Homework

• Homework, #1: problems
  solutions
  
• Homework, #2: problems
  solutions
  
• Homework, #3: problems
  solutions
  
• Midterm exam, Midterm exam solutions
• Homework, #4: problems
  solutions
  
• Homework, #5: problems
  solutions
  
• Homework, #6: problems
  solutions
  
• Final exam, Final exam solutions