The Universal Composite Fermion Hall Conductance at $ν=1/2$

Abstract

We show that at electronic filling factor $ν=1/2$, the lowest Landau level constraint implies that at any temperature, and in the presence of {\it any} amount of particle-hole symmetric disorder, the {\it composite fermion} Hall conductivity is precisely $-e^2/2h$. (The electronic Hall conductivity is $e^2/2h$.) This is inconsistent with the response of a composite Fermi liquid in {\it zero} effective magnetic field. We also examine perturbatively the nature of the putative composite Fermi liquid in the case in which the bare particles are anyons with ``nearly'' Fermi statistics.