Transport and dynamic properties in
the Fermion-Chern-Simons picture.

Results for f=1/2 (with no impurities)
Electron system is
compressible.
Fluctuations
in the electron density
relax very slowly
at long
wavelengths.
Relaxation
rate obeys
γ
∝
q
2
,
for unscreened Coulomb interactions
γ
∝
q
3
,
for short range interactions.
Longitudinal electrical conductivity at finite wave vector
obeys
(in
absence of impurities)
σ
xx
(
q
)
∼
(e
2
/4h) (
q
/
k
F
)
(Nonlocal)

Longitudinal conductivity
σ
xx
(
q
) is
measured in a Surface Acoustic Wave
experiment
q= wavevector of sound wave.
Anomaly in
SAW propagation at f=1/2,
was observed by Willett and
coworkers in 1990 and subsequent experiments.
Find
: conductivity increases linearly with q when 1/q is smaller than mean free
path for scattering of composite fermions due to impurties --
as predicted by
Fermion+Chern-Simons theory.
Quasiparticles
can travel in a straight line
for distances of order of a micron,
100 times larger
than the
cyclotron radius
for electrons in the applied magnetic
field

Strengths and weaknesses of
Fermion-Chern-Simons approach

Also: Boson + Chern-Simons theory
Transform electrons to bosons
by attaching an
odd
number of
Chern-Simons
flux quanta
to each particle.
Brings out
analogies between quantum Hall effect and superfluidity.

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- Fall '13
- BertrandI.Halperin
- Physics, wave function