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

TL;DR

This paper demonstrates that at filling factor =1/2, the composite fermion Hall conductance is universally ^2/2h regardless of temperature or disorder, challenging the conventional composite Fermi liquid picture.

Contribution

It establishes a universal composite fermion Hall conductance at =1/2, highlighting a fundamental inconsistency with the standard Fermi liquid response.

Findings

Composite fermion Hall conductance is exactly -e^2/2h at =1/2.

This conductance is invariant under temperature and disorder.

The result conflicts with the expected zero effective magnetic field response.

Abstract

We show that at electronic filling factor $\nu=1/2$, 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.