Frictional magnetodrag between spatially separated two-dimensional electron systems: Coulomb versus phonon mediated electron-electron interaction

We study the frictional drag due to Coulomb and phonon mediated electron-electron interaction in a double layer electron system exposed to a perpendicular magnetic field. Within the random phase approximation we calculate the dispersion relation of the intra Landau level magnetoplasmons at finite temperatures and distinguish their contribution to the magnetodrag. We calculate the transresistivity $\rho_{Drag}$ as a function of magnetic field $B$, temperature $T$, and interlayer spacing $\Lambda$ for a matched electron density. For $\Lambda =200$ nm we find that $\rho_{Drag}$ is solely due to phonon exchange and shows no double-peak structure as a function of $B$. For $\Lambda =30$ nm, $\rho_{Drag}$ shows the double-peak structure and is mainly due to Coulomb interaction. The value of $\rho_{Drag}$ is about 0.3 $\Omega$ at T=2 K and for the half-filled second Lanadau level, which is about 13 times larger than the value for $\Lambda =200$ nm. At lower edge of the temperature interval from 0.1 to 8 K, $\rho_{Drag}/ T^{2}$ remains finite for $\Lambda =30$ nm while it tends to zero for $\Lambda =200$ nm. Near the upper edge of this interval, $\rho_{Drag}$ for $\Lambda =30$ nm is approximately linear in $T$ while for $\Lambda =200$ nm it decreases slowly in $T$. Therefore, the peak of $\rho_{Drag}/ T^{2}$ is very sharp for $\Lambda =200$ nm. This strikingly different magnetic field and temperature dependence of $\rho_{Drag}$ ascribe we mainly to the weak screening effect at large interlayer separations.