Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data

Abstract

The Hamiltonian Theory of the fractional quantum Hall effect is an operator description that subsumes many properties of Composite Fermions, applies to gapped and gapless cases, and has been found to provide results in quantitative accord with data on gaps, relaxation rates and polarizations at temperatures of $300mK$ and above. The only free parameter is $\lambda$, which is related to the sample thickness and appears in the Zhang-Das Sarma potential $v(q) = {2\pi e^2\over \kappa q} e^{-ql\lambda}$ where $l$ and $\kappa $ are the magnetic length and dielectric constant. Here we examine the recent data of Tracy and Eisenstein on the nuclear magnetic resonance relaxation rate at filling factor $\nu=\half$ deduced from resistivity measurements at temperatures as low as $45mK$. We find that their results can be satisfactorily described by this theory, if in addition to a $v(q)$ with $\lambda \simeq 2$, a constant disorder width $\Gamma\simeq 100 mK$ is incorporated.