fqhe-268pt3 lecture - Transport and dynamic properties in the Fermion-Chern-Simons picture Results for f=1\/2(with no impurities Electron system is

fqhe-268pt3 lecture - Transport and dynamic properties in...

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Transport and dynamic properties in the Fermion-Chern-Simons picture.
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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)
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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
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Strengths and weaknesses of Fermion-Chern-Simons approach
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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

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