For this final homework write a short (it need not be more
than one typed page) description in your own words of ONE of the following topics or a
different topic that you choose.
If you want to choose a different topic,
you must get my approval of the topic by Dec. 4.
You can send a suggested topic by email to me at rmartin@uiuc.edu or you can make an
appointment by email.
(I will be out of town
November 29 (leaving soon after class) through Dec. 3. I
will check by email sometimes during that period.)
An discussion of some aspect of nanostructures following
the material in the presentations of Prof. Nayfeh or Prof. Budakain.
In this case you should look up at least one of their papers as a reference
for your description.
A summary of the phenomena and understanding of the
integral quantized Hall
effect. There is a good description in Kittel and you may use
other sources. It will be sufficient to choose one of the following:
The experimental setup and the analysis of the conductivity tensor
in the presence of a magnetic field. This would include the analysis showing that
one expects an "effective conductance that is infinite" when the
Hall effect is quantized.
The arguments due to Laughlin that show that the effect is
quantized due to gauge invariance so that it is rigorously quantized
and is not modified by sample conditions, temperature, etc. (Note that a
description of gauge transformations is given in an appendix of Kittel
and there is an analogy to flux quantization in a superconductor.)
A summary of the phenomena and understanding of superconductivity. There
is a good description in Kittel, and I recommend a book "Superconductivity of
Metals and Alloys" by P. de Gennes which is on reserve in the physics library.
(It is on reserve for another course, but you can request it.)
It will be sufficient to choose one of the following:
The two characteristic length scales in superconductivity. The
physical reasoning that leads to each length and the relation to
type I and type II superconductors.
The phenomena and understanding of flux quantization in type
II superconductors. This provides a definitive measurement showing that
superconductivity involves pairs of electrons. (Note that
descriptions of gauge transformations and the Landau-Ginzberg
equations are given in an appendix of Kittel
and there is an analogy to integral quantized Hall
effect.)
The BCS theory of superconductivity caused by electron-phonon
interactions. You do NOT need to give the mathematical derivation,
but only a summary of the main ideas.
A description of the De Haas-van Alphen effect
in metals (Ch 9 of Kittel). The effect is due to quantization of
electron orbits in a magnetic field and it is is the most definitive measurement
of the Fermi surface in a metal. There is an interesting relation to
the integral quantized Hall effect, which can be seen in terms
of the quantization of electron orbits.
A summary in your words of the reasons why Bragg peaks are
NOT broadened in a crystal due to thermal vibrations of the atoms.
Despite the fact that the atoms are displaced from their ideal positions
at lattice sites, the Bragg peaks are still sharp (delta functions in
the limit of an infinite crystal). The effect of thermal vibrations
is to reduce the strength of the Bragg scattering, which is described
by the Debye-Waller factor. is reduced. . effects even thou De Haas-van Alphen effect
in metals (Ch 9 of Kittel). The effect is due to quantization of
electron orbits in a magnetic field and it is is the most definitive measurement
of the Fermi surface in a metal. There is an interesting relation to
the integral quantized Hall effect, which can be seen in terms
of the quantization of electron orbits. State in your own words the argument for why a persistent
current can flow for very long times (times that could be longer than
the age of the universe!) in a ring of a type 1 superconductor.
A description of a scattering experiment (neutron scattering, light scattering,
etc.0 that measures energies of phonons in a crystal.
A description of the electronic bands in carbon nanotubes.
Many of the interesting effects are due to the fact that
a sheet of graphene has a point Fermi surface (actually three points
that are related by symmetry where the filled and empty bands
touch). You do NOT need to derive this fact; the proof is simple
but rather technical.
The topics above are just suggestions. You may vary the topic
or choose a different topic PROVIDED I APPROVE THE TOPIC BY DEC. 4 as
stated above.