QM4: Quantum Hall and Many Body Effects

Module title: Quantum Hall and Many Body Effects (QM4)

Module convenors: Andy Schofield and Nicholas d'Ambrumenil

The course structure is as follows:
  • Lecture 1 (AJS): Quantum criticality in itinerant Fermi systems: Fermi liquid theory and the Reizer singularity
  • Lecture 2 (Nd'A): Kondo Effect and Heavy Fermions
  • Lecture 3 (Nd'A): Quantum Hall Effect
  • Lecture 4 (AJS): Quantum criticality in itinerant Fermi systems: SCR and Hertz Millis theory
  • Lecture 5 (AJS): Quantum criticality in itinerant Fermi systems: What is going wrong?

Module aims:

To explore quantum phenomena in interacting many-particle systems.

Learning objectives:

At the end of the module you should understand better the background to some current major issues in condensed matter physics.


Kondo Effect
The Anderson impurity, solution for the ground state in the large N limit. The Kondo resonance. Scattering theory and phase shifts: elastic scattering rate, Friedel sum rule, Wigner delay time. The quasiparticle interpretation valid for T \ll T_K and unitarity limit. Kondo lattices and the idea of the coherence temperature.

Quantum Hall Effect
Modulation doped heterostructures and the measurements. Zeros in wavefunctions in a magnetic field. Landau levels (LL) and projection onto a LL. Laughlin's wavefunction and quasiholes. Composite fermions and the singular gauge transformation. Effective mass as a parameter to fit to experiment/exact diagonalization studies. Wavefunctions in higher LL's, the pfaffian. Mention of degeneracy and non-abelian statistics.

Quantum Criticality in Itinerant Fermi Systems
Derivation of the effective (Hertz-Millis) action for a system close to a zero temperature ordering transition (quantum critical point). Introduction of the slowly varying field characterising the order via the Hubbard-Stratonovic transformation. Integrating out the fermions, expansion in the coupling to fermions. Importance of the term linear in frequency and its relation to relaxation . Comparison with standard Landau theory of phase transitions at non-zero temperature. Scaling analysis of the action and identification of the temperature-controlled and order-controlled parts of the phase diagram. Relation of Tc to the fourth order term. Temperature-dependence of heat capacity and resistivity, comparison to experiments.

Academic year: 
13/11/2009 - 11:00