Syllabus for PHZ7428, Topics in Theoretical Physics (High-Tc Superconductivity), Spring 1995

Peter Hirschfeld

Course Description. The problem of high-temperature superconductivity (HTSC) has occupied the attention of a remarkably large portion of the condensed matter physics community since the discovery of the cuprate superconductors in 1986. Part of the reason for this lies in the obvious promise of radical new technology, which once seemed imminent but now appears further off. Experimental and theoretical studies of the HTSC have also been driven by the enormous challenge of the fundamental problem, howe ver. For example, even the simplest models of the two-dimensional Cu-O planes are insoluble since they involve strongly interacting fermions, and the actual materials are considerably more complicated. Furthermore, the high-Tc problem is difficult because it encompasses subproblems from nearly all areas of condensed matter physics, and parts of what has traditionally been high-energy physics as well. Nevertheless, a great deal has been learned in the past ten years. It is the aim of this course to summarize the current state of this understanding and distill some basic principles from the large and confusing literature. While the primary focus will be on theory, probably half the lecture/discussion time will be spent reviewing experiments. No axes will be ground.

Tentative Requirements: 1 30-minute oral presentation, 1 ``proposal" paper. The first will involve a simple summary of some aspect of HTSC experiment or theory, in ``journal club" format, to be integrated into the lectures. The second will ideally be the precursor to a publishable research paper, i.e. the identification of an important unanswered question, an idea for an experiment or theoretical approach to address this question, and preliminary design or calculation to support the proposed approach. Depending on class interest, groups may be formed to work on these papers.

• Bibliography
• Other resources

1. History of High-Tc: why the fuss?

   Suggested reading: Hoddeson, Bednorz & Mueller Nobel Lectures

2. Normal Metals
   1. Fermi liquids
   2. Green's functions for normal metals and interacting systems
   3. Electron-phonon system

   Suggested reading: Baym & Pethick, Rickayzen2, Schrieffer, Mahan

3. Classic superconductors: BCS Theory
   1. Cooper instability
   2. BCS model Hamiltonian and Gorkov equations
   3. Critical temperature and thermodynamics
   4. Electrodynamics
      1. Meissner effect
      2. dynamical conductivity
   5. Disorder: Anderson theorem

   Suggested reading: Tinkham, Schrieffer, Rickayzen1&2

4. Ginzburg-Landau theory
   1. GL limit & phenomenological Hamiltonian
   2. Gorkov derivation from BCS
   3. Type I/Type II superconductors
   4. Hc2, Abrikosov lattice
   5. vortices
   6. Lawrence-Doniach theory

   Suggested reading: Tinkham, de Gennes

5. Mechanisms --3 lectures starting Fri. Mar. 1
   1. Strong coupling / crossover to Bose condensation
   2. Excitons à la Little, Allender-Bray-Bardeen
   3. Electronic pairing, spin fluctuations, triplet pairing and all that

   Suggested reading: Ginzburg, Anderson1, Scalapino

6. Electronic structure --2 lectures starting Fri. Mar. 8

   Note 2-week recess starting Mar. 11 for a) spring break and b) APS March meeting. Reconvene Mar. 25

   1. Phase diagrams
   2. Theoretical electronic structure calculations
   3. 2-band Hubbard models; Trans. Metal Oxides
   4. ARPES: technique and band structure

   Suggested reading: Plakida, Brenig

7. Transport properties in normal state --3 lectures starting Mar. 27
   1. Resistivity
   2. Optics
   3. Hall effect
   4. Breakdown of FL theory
   5. Small energy scale theories
   6. Luttinger model
   7. Gauge fields and Reizer singularity

   Suggested reading: Iye article in Ginsberg, VIII, Anderson2, Voit, P.A. Lee 1

8. Magnetic properties --3 lectures starting April 3
   1. Heisenberg model: spin wave theory and beyond
   2. Spectroscopy of insulators
   3. Hubbard and t-J models
   4. One hole in antiferromagnet: Nagaoka, Brinkman-Rice, etc.
   5. Spin gap puzzle: susceptibility and NMR experiment
   6. Quantum critical scenario
   7. ``Ladder" compounds and theories

   Suggested reading: Kampf, Millis, Sokol, P.A. Lee 2, Dagotto

9. Unconventional Superconductivity --3 lectures starting April 10
   1. Definition of unconventional superconductivity
   2. Microscopic arguments for $d_x^2-y^2$ state
   3. Extended-s states
   4. Low-temperature properties, density of states
   5. Josephson tunneling
   6. Impurity effects

   Suggested reading: Scalapino, Sigrist and Ueda, Hirschfeld

10. Experimental superconducting state properties --3 lectures starting April 17
    1. Photoemission
    2. Optics,
    3. NMR
    4. Neutrons
    5. Josephson effect
    6. Impurity effects
    7. Josephson effects

    Suggested reading: Dessau, Tanner, Slichter, Mook,Keimer,v. Harlingen, Kirtley,

11. HTSC in magnetic fields --1 lecture on April 24
    1. Experimental phase diagram & irreversibility line
    2. Vortex glass ideas
    3. Competing theories

    Suggested reading:

12. ``Conclusions": review of competing paradigms for HTSC --1 lecture on April 26