Measurements of Composite Fermion Conductivity Dependence on Carrier Density

TL;DR

This study experimentally investigates how the conductivity of composite fermions in GaAs heterostructures depends on carrier density, revealing an exponent close to 1, which bridges theoretical predictions for different magnetic field regimes.

Contribution

First experimental measurement of composite fermion conductivity dependence on carrier density at specific filling factors in high-quality heterostructures.

Findings

Exponent α ≈ 1 for conductivity dependence.

Results lie between strong and weak random magnetic field predictions.

Comparison with theory discussed.

Abstract

We present the first experimental study of the carrier density dependence of the composite fermion conductivity $\sigma^{CF}_{xx}$ at Landau level filling factors $\nu= {1/2}$ and $\nu= {3/2}$ in high-quality front-gated GaAs/Al$_{0.33}$Ga$_{0.67}$As heterostructures. Extracting $\alpha$ from the power law ln$(\sigma^{CF}_{xx}) \propto$ ln$(n_e)^{\alpha}$ shows that $\alpha \approx 1$. The measured ${\alpha} \approx 1$ is placed between the predicted value 3/4 in the strong random magnetic field regime, and 3/2 in the weak random magnetic field regime. Comparisons between our results and theory are discussed.