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

TL;DR

This paper demonstrates that under specific conditions, the composite fermion Hall conductance at filling factor 1/2 is constrained to a universal value, impacting the understanding of composite Fermi liquids in quantum Hall systems.

Contribution

It establishes a universal constraint on the composite fermion Hall conductance at $ u=1/2$ considering particle-hole symmetry and vanishing effective mass.

Findings

Composite fermion Hall conductance is constrained to -1/2 e^2/h.

Results imply a specific nature of the composite Fermi liquid at $ u=1/2$.

Particle-hole symmetric disorder influences the conductance constraint.

Abstract

We show that in the limit of vanishing bare electron effective mass, and in the presence of particle-hole symmetric disorder (which can be of vanishing strength), the composite fermion Hall conductance is constrained to be $-{1\over 2}\frac{e^2}{h}$. We discuss the implications of this results for the existence and nature of a composite Fermi liquid in the lowest Landau level.