Condensed Matter Physics 238A
Fall 2008
Tuesday &
Thursday, 9:30-10:50pm
FRH 2111
Instructor:
Dr. Sasha Chernyshev, Associate Professor
Office: FRH 2158
Phone: (949)-824-6440
E-mail: sasha@uci.edu
Web page: http://www.physics.uci.edu/faculty/chernyshev.html
Office hours: open office policy
Introduction
This course is the first in a sequence of three Condensed Matter
Physics courses.
It covers several broadly related topics. In all of them we use the
quantum mechanics
and statistical physics to understand the processes in solids
(condensed matter).
Topics to be covered
- Crystal structures
- Periodic structures, idea of crystals
- Bravais lattices, unit cells
- Point group symmetries
- 2D, 3D Bravais lattices
- Close packing, crystal formation
- lattices with basis
- Inverse lattice, vectors, symmetries
- Bragg planes, indices
- Scattering problem, Bragg's law, Ewald's construction
- X-rays, electrons, neutrons, physical restrictions
- surfaces, experiments (LEED, STM, etc.)
- Alloys, Phase diagrams
- Phase separation, role of dynamics
- Correlation functions, structure factor
- Long-range order, order parameter
- liquids, amorphous solids, structure factor
- Glasses, open issues
- Liquid crystals, classification
- quasicrystals
- Electronic properties of solids, bands
- Cohesion in solids, types of crystals
- Basic Hamiltonian, adiabatic approximation
- picture of non-interacting Fermi-gas
- Ground state properties, useful quantities (kF, rs, EF)
- Defining a "good" metal, density argument. Large rs, Wigner
crystal
- Density of states
- Total energy, specific heat, statement of the problem for
T>0
- Sommerfeld formalism
- Specific heat, T-dependence of mu, Sommerfield constant
- Translational invariance, waves in crystals, Bloch's theorem
- Folding to the Brillouin zone
- "nearly-free" electrons, Schroedinger E. in momentum space
- Perturbation theory in momentum space
- Role of Bragg scattering near BZ boundaries, band formation
- van Hove singularities, Kronig-Penney model
- Folding of the Fermi surfaces, Harrison construction
- Tight-binding, idea, justification, bands
- Derivation from Block-like construction, tunneling amplitude
- hopping integrals, Hamiltonian, effective mass
- Brief overview of the periodic table
- role of e-e interaction, Mott effect, idea of DFT
- Elements of the
theory of metals
- Zeeman effect and Pauli paramagnetism, susceptibility
- Quantization of the orbital motion, Landau levels.
- Landau diamagnetism, oscillation of magnetization
- de Haas van Alphen effect, extremal orbits, measurements of the Fermi surfaces
- Aharonov-Bohm effect
-
Recommended Books
- M. P. Marder, Condensed matter physics,
published
by John Wiley and Sons, Inc., 2000.
- Principles of the Theory of Solids, by J. M. Ziman,
Cambridge University Press; 2 edition (1979).
- Solid State Physics, by N. W. Ashcroft and N. D.
Mermin, Saunders College Publishing (1976).
- Quantum theory of solids, by C. Kittel, published by
John Wiley and Sons (1963).
Extra material
Homeworks
Homeworks will be assigned weekly. They will be collected on the "target"
dates (announced separately) and graded.
The homework assignments
will be due at the beginning of class.
The grade will be based on your homework and presentation on one of the
condensed matter topics.
- Homework, week #1: Marder:
problems 1.4 and 2.2
solutions
- Homework, week #2: Marder:
problems 3.2 and 5.2
solutions
- Homework, week #3: Marder:
problems 6.2, 6.4, + extra
solutions
- Homework, week #4: Marder:
problems 6.6(a)-(c) and 6.8
solutions, numerical part
- Homework, week #5: Marder:
problems 8.1(a)-(f)
solutions
- Homework, week #6-7: Marder:
problems 7.3(b),(c),
problem 7.4: clarifications: (1) use U0=(1/3)*E_1, where E_1 =
hbar^2 G1^2/2m, with G1=2*pi/a, to make the equation dimensionless.
(2) plot the result of your
calculations in *repeated* zone scheme as in Fig.7.6, so 3-4 bands are
distinguishable.
problem 8.6: clarifications: (1) this is not a Bravias lattice. (2) it is useful to picture values
of the on-site potential
(last term in H) for different "l".
(3) obtain explicitly the algebraic
equation that follows from "the simple matrix equation", and then
solve it (numerically or
otherwise).
Extra credit problem:
problem "7.4++": Solve Kronig-Penney model for 1D
Bravais lattice analytically. This involves transforming summation
over G-vectors to a contour integral over a function with poles
at G_n, changing the contour, evaluating integral, etc.
The result will allow to express q vs
E, not E vs q.Plot the resulting q*a vs E/E1 for
U0=(1/3)*E_1,
where E_1 = hbar^2 G1^2/2m,
with G1=2*pi/a as before.
Note: -- do not quote the result of
analytic summation from Mathematica, etc., I want to see the actual work.
solutions, numerical part
Extra credit solution
- Homework, week #8:
problems
solutions