Condensed Matter
Physics I
PHYS 502, Spring
2012
Instructor:
Prof. M. Franz
[Henn 336, franz(at)physics(dot)ubc(dot)ca]
Lectures: Tu & Th
12:30-14:00 in Hennings 302
Office hours: We 13:30-14:30 and by appointment
Course TA:
Ryan McKenzie
[Henn 414, ryanmck_van(at)hotmail(dot)com]
TA office hours: Tue
14:00-15:00 and by appointment
Textbook (available in the bookstore):
- "Solid State Physics" by
Ashcroft & Mermin
Other useful texts (placed on
reserve in the library):
- "Quantum Theory of Solids", 2nd Revised
Edition by Charles Kittel
- "Advanced Solid State Physics" by Phillips
- "A Quantum Approach to Condensed Matter Physics" by Taylor &
Heinonen
- "Condensed Matter Physics" by Marder
Grades will be determined based
on biweekly assignments, midterm, and the final exam (30/30/40).
Course
announcements:
- First lecture will take place on Thursday January 5.
- Midterm will take
place on March 8. It will consist of a short in-class test (see last year's exam here)
and a take-home exam due back on March 12. The in-class part is closed
books, closed notes, about 30min in length.
- The final exam will
take
place on April 11. It will consist of a short in-class test
and a take-home exam due back on April 13. The in-class part is closed
books, closed notes, about 40min in length. The exam covers all the
material discussed in the course.
- Office hours prior to the final exam will be as follows: Tu and
We 11-12noon.
Assignments:
*This can be viewed as a "test assignment". If you can solve it
without great difficulty you are ready for this course. If not, then
you should take PHYS 474 first.
Working out the assignments is perhaps the single most important aspect
of this course, absolutely essential for your understanding of the
material. In order to receive
credit assignment
must be handed in by the end of the lecture on the due date. If
you foresee a serious conflict that might prevent you from completing
the problems by the due date please let me know ahead of time. I will consider
extending the due date if the conflict affects several students in the
class. In fairness to other students who completed assignment on
time last minute requests for extension will not be granted.
Course
outline:
This course provides a graduate-level introduction to the fundamental
concepts of condensed matter physics. It
is assumed that students are familiar with the basic concepts of solid
state physics (e.g. crystalline lattices, Bloch bands,
Drude model etc.) as covered in a typical undergraduate solid state
course such as UBC's PHYS 474. In addition, working knowledge of
quantum mechanics, basic statistical physics and thermodynamics will be
assumed.
- Introduction: Solids as interacting quantum many-body systems
- Basic Hamiltonian, CM `theory of everything'
- Born-Oppenheimer approximation
- Second quantization for fermions and bosons
- Electrons in solids
- Free electron gas model, Jellium
- Interactions, Hartree-Fock approximation
- Random phase approximation, screening
- Boson systems
- Bogoliubov theory of helium
- Phonons
- Magnons
- Electrons in a periodic potential
- Bloch theorem
- Nearly free and tight binding approximations
- Dynamics of Bloch electrons, metals vs. insulators
- Outline of the Density functional theory
- Semiclassical theory of conduction in metals
- Non-equilibrium distribution function
- Relaxation time approximation
- Electrical and thermal conductivity, thermoelectric effects
- Effects of magnetic fields
- Electron-phonon interactions
- The Frolich Hamiltonian
- Phonon frequencies and Kohn anomaly, Peierls transition
- Polarons and mass enhancement
- Elements of superconductivity
- Origin of attractive interaction between electrons
- BCS Hamiltonian, pairing instability, Bogoliubov transformation
- Transition temperature, energy gap, ground state wavefunction
- Meissner effect, tunneling experiments, flux quantization and
the Josephson effect
- Depending on
time and student interest some of the following
additional topics may be discussed:
- Introduction to mesoscopic physics
- Quantum Hall effect (integer and fractional)
- Kondo effect
- Basic one-dimensional physics, Luttinger liquids, bosonization