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

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 $s = [\partial\tau/ \partial\varepsilon] (\varepsilon_F)$.