PHYS 561
Advanced Topics in Condensed Matter Physics
Lecturer: T. Hakioğlu
Outline: This one semester course is a crash course on condensed matter field theory and fundamental low temperature collective effects in the bulk and low dimensional systems. The course starts with methodology followed by its applications to certain physical systems. In particular, the equivalence of the standart many body Green’s function techniques using canonical second quantization and the path (functional) integral quantization will be shown. In most of the course, the Green’s function technique at zero and finite temperatures as well as the thermodynamical quantities will be derived using the path (or functional) integrals.
Part.1: Methodology
1.1: Bosonic and Fermionic Harmonic Oscillator Coherent States
1.2: Feynman Path Integration
1.3: Field Quantization of Bosonic and Fermionic fields
1.4: Green’s Functions at Zero and Finite Temperature
1.5: Bosonic and Fermionic Functional Integration
1.6: Statistical Mechanics of Fields and Functional Integration
1.7: Interactions (Partition Function and Linked Cluster Expansion)
Part.2: Physical Cases:
2.1: Landau-Fermi Liquid Theory
2.2: Electron-Phonon interactions
2.3: Electron gas in 3D and 2D
Part.3: Theory of Type-I and Type-II Superconductivity
Part.4: Theory of Superfluidity
Part.5: Atomic Gases and Bose Einstein Condensation
Part.6: Quantum Hall Effect: IQHE, FQHE
Part.7: QHE and Excitonic Coherence in bilayers
Part.8 Theory of Superconducting Devices
Some Term Projects:
Student is free to choose any topic below fort the term project. He/she can also bring his/her own topic as an alternative choice to be examined and decided by
the lecturer.
- Bose-Hubbard Model
- DC and AC Josephson effect in bilayer exciton Quantum Hall systems
- Exciton condensation in rotating laser field
- Kosterlitz Thouless Phase Transition
- Self consistent many body effects in the single layer IQHE
- QHE in Graphene
- Heavy fermion Superconductivity
- Triplet superconductivity
- Phenomenological theory and experimental verification of tunneling between SC and normal metals, Andreev Reflection
- Giant magnetic resonance in FNF, FSF interfaces
- Migdal-Eliashberg Strong Coupling theory of BCS Superconductivity
- Measurement of the magnitude and the symmetry of superconducting gap
- Angle Resolved Photoemission Spectroscopy (ARPES)
- Time resolved Photoemission Spectroscopy
- Raman spectroscopy
- Experimental Measurement techniques of the Subnikov-de-Haas oscillations
The students are required to work on certain homework problems which will be designed to be pedagogical without extensive labor. The solutions to the homework problems will be presented by the students in the class every week on a rotating basis. The projects are replacements of the Midterm and Final examinations.