Solid State (II)


Course Syllabus pdf file

Lecture notes

  • More is different The famous paper by P. W. Anderson.
  • Supplemental Material: Review single-particle physics
  • Supplemental Material: Brief introduction to 2nd quantization

    Landau Fermi liquid theory -- Phenomenology
  • Lecture 1 : Quasi-particles, Landau interaction function
  • Lecture 2 : Renormalization to physical quantities, Pomeranchuk instability
  • Lecture 3 : Boltzman equation, zero sound, spin transport
  • Further reading : A theoretical description of the new phases of liquid 3He, A. J. Leggett, Rev. Mod. Phys. 47, 331 (1976).
  • Further reading : Fermi liquid instability in the spin channel, C. Wu et al, PRB 75, 115103 (2007),
    and Dynamic generation of spin-orbit coupling, C. Wu and S. C. Zhang, PRL 93, 036403 (2004).
  • Further reading : Spin-orbit coupled Fermi liquid theory of ultracold magnetic dipolar fermions, Y. Li and C. Wu, Phys. Rev. B 85, 205126 (2012)
  • More information and slide

    Interacting electron gas
  • Supplemental Material: Hartree-Fock theory
  • Lecture 4 : Lindhardt response, RPA, plasmon
  • Lecture 5 : Screening
  • Lecture 6 : Density functional theory

  • Lecture 7 : Quantum magnetism -- Heisenberg model

    Formalism: Green's function, path integrals, operators,
  • Lecture 8 : Operator formalism, response functions
  • Lecture 9 : Path integral for functional fields and fermions
  • Lecture 10 : Perturbation theory for fermions
  • Lecture 11 : RPA
  • Lecture 12 : Correlation energy
  • Lecture 13 : Life time, Fermi surface
  • Lecture 14 : Spin wave in metals

    Supplemental Materials: Landau Fermi liquid theory -- Microscopic theory
  • Microscopic theory (I) : Vertex functions.
  • Microscopic theory (II) : Ward Identities and Luttinger theorem.
  • Microscopic theory (III) : More

    Phonons
  • Supplemental Material: Acoustic phonons - long-wave length method, elasticity
  • Supplemental Material: Optical phonons - polariton, Huang's Equation
  • Lecture 15 : Electron-Phonon interaction

    Superconductivity
  • Supplemental Material: Phenomenology of superconductivity
  • Lecture 16 : BCS-mean field theory
  • Lecture 17 : Thermodynamics, McMillan formula, linear response and coherence factors
  • Lecture 18 : GL theory, EM response, and dirty superconductor
  • Supplemental Material : Functional field method to GL equation and EM response
  • Supplemental Material : Unconventional Superconductivity
  • Supplemental Material : Phase sensitive detection to Unconventional Superconductivity
  • Supplemental Material : p-wave, He-3 A and B, d-vectors, topological edge stades

    Supplemental Materials: Superfluidity
  • Mean-field theory for superfluidity
  • Path integral for superfluidity
  • Low dimensional superfluidity
  • Renormalization group theory for K-T transition
  • EM response of charged superfluidity

    More
  • Kondo problem
  • Disordered electrons
  • Transport

    Howework assignment
    HW1 pdf Review on 2nd quantization and HF, due on Jan 22 class. If you have difficulty, check supplemental materials. Solution posted on Jan 22.

    HW2 pdf You may skip Problem 1.3, for which you need the knowledge of Thomas-Fermi screening length. Due on Jan 31 (Thur) class. Solution posted on Feb 5.

    HW3 pdf Due on Feb 19 (Tues) class. Solution Posted on Feb 21.

    Midterm and Final

    Midterm the pdf file . Due on Feb 28 in class. You only need to do Problems 1 and 2, i.e., page 1 to 4. Solutions posted on March 2 .







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    Last modified: Jan 7, 2010.