Can Hall drag be observed in Coulomb coupled quantum wells in a magnetic field?

TL;DR

This paper demonstrates that Hall drag can be observed in Coulomb-coupled quantum wells under a magnetic field at high temperatures, challenging prior assumptions that it was impossible.

Contribution

It reveals that Hall drag is observable when intra-layer transport time has energy dependence, providing a new understanding of Coulomb drag phenomena in magnetic fields.

Findings

Hall drag can be observed at high temperatures with energy-dependent transport times.

The ratio of Hall to longitudinal transresistivities scales as T^2 B s.

Elementary arguments against Hall drag observation are shown to be incorrect.

Abstract

We study the transresistivity $\tensor\rho_{21}$ (or equivalently, the drag rate) of two Coulomb-coupled quantum wells in the presence of a perpendicular magnetic field, using semi-classical transport theory. Elementary arguments seem to preclude any possibility of observation of ``Hall drag'' (i.e., a non-zero off-diagonal component in $\tensor\rho_{21}$). We show that these arguments are specious, and in fact Hall drag can be observed at sufficiently high temperatures when the {\sl intra}layer transport time $\tau$ has significant energy-dependence around the Fermi energy $\varepsilon_F$. The ratio of the Hall to longitudinal transresistivities goes as $T^2 B s$, where $T$ is the temperature, $B$ is the magnetic field, and $s = [\partial\tau/ \partial\varepsilon] (\varepsilon_F)$.