PHYS 568 A: Theory of Solids

Spring 2023, 568A, Theory of solids.  MW 2:00-3:20.  

Instructor Boris Spivak, office B440.

Office hours after each lecture. }

Grading: C/NC.

There will be no final exam. Grading will be based on  HW. 

 I will use the following books :

 Michael Marder, Condensed Matter Physics.

E.M. Lifshitz, L.P. Pitaevskii,  Statistical physics||,

S.M. Girvin, Kun Yang, Modern condensed matter physics. 

and reviews on different subjects. 

 Tentative syllabus.

1. Berry phase. 

2. Quantum Hall effect. 

a. Integer quantum Hall effect.}

Single particle band structure in the presence of magnetic field.  Magnetic Bloch bands. 

Kubo formula for conductivity and quantization of $\sigma_{xy}$ in magnetic Bloch bands. Topological interpretation of QH effect, Chern numbers. 

Integer quantum Hall effect in the presence of scattering potential. Why disorder and localization are important. 

Semiclassical picture of QH.

Quantum Hall effect without Landau levels, Haldane model.

Integer anomalous quantum Hall effect. 

b. Fractional quantum Hall effect.

Laughlin wave function. Fractional statistics.  Chern-Simons formulation of the theory of quantum hall states. Even and odd denominators, non-abelian quasiparticles. 

c. Stripe phases. 

3. Weyl and Dirac metals. Anomalous velocity in semiclassical equations of motion of electron in a lattice. Chiral anomaly. 

4. Topological insulators.

Kane-Mele model, $Z_{2}$ characterization of the topological insulators. 

5.Topological superconductors.

6. Instabilities of Fermi liquids.}

Pomeranchuk instabilities.

Peierls instability.  Su-Schrieffer-Heeger model, an example of spin and charge separation.