Coulomb drag in compressible quantum Hall states

TL;DR

This paper investigates Coulomb drag in quantum Hall states near filling factors 1/2, revealing a large transresistivity with a unique temperature dependence of T^{4/3}, and compares electronic and composite fermion perspectives.

Contribution

It provides a detailed analysis of Coulomb drag at various filling factors, highlighting the impact of wave-vector dependent conductivity and clarifying the physical origin of the drag.

Findings

Transresistivity is significantly larger near ν=1/2 compared to zero magnetic field.

The temperature dependence of transresistivity follows a T^{4/3} law.

Results suggest Coulomb drag is primarily due to electronic interactions, not Chern-Simons effects.

Abstract

We consider the Coulomb drag between two layers of two-dimensional electronic gases subject to a strong magnetic field. We first focus on the case in which the electronic density is such that the Landau level filling fraction $\nu$ in each layer is at, or close to, $\nu=1/2$. Discussing the coupling between the layers in purely electronic terms, we show that the unique dependence of the longitudinal conductivity on wave-vector, observed in surface acoustic waves experiments, leads to a very slow decay of density fluctuations. Consequently, it has a crucial effect on the Coulomb drag, as manifested in the transresistivity $\rho_D$. We find that the transresistivity is very large compared to its typical values at zero magnetic field, and that its temperature dependence is unique -- $\rho_D \propto T^{4/3}$. For filling factors at or close to $1/4$ and $3/4$ the transresistivity has the same $T$-dependence, and is larger than at $\nu = 1/2$. We calculate $\rho_D$ for the $\nu=3/2$ case and propose that it might shed light on the spin polarization of electrons at $\nu=3/2$. We compare our results to recent calculations of $\rho_D$ at $\nu=1/2$ where a composite fermion approach was used and a $T^{4/3}$-dependence was obtained. We conclude that what appears in the composite fermion language to be drag induced by Chern-Simons interaction is, physically, electronic Coulomb drag.