A Physical Picture for the Negative Drag in High Landau Levels

Experimental investigation of the longitudinal drag resistivity, $\rho^D$, of a bi-layer subjected to a strong magnetic field in the regime of large filling factors found an anomalous behavior at low temperatures $T$: $\rho^D$ depends non monotonously on $T$ and becomes negative when the filling factors of the two layers differ by an odd number. A calculation of $\rho_D$ within the framework of the self consistent Born approximation was generally consistent with the experiment; nevertheless, it left the physical picture obscure. We employ the exact eigenstates method to unravel that picture. We find the oscillating sign of $\rho^D$ to originate from the effect of disorder on the relation between an adiabatic momentum transfer to an electron and the displacement of its position. For localized states a momentum transfer $\bf q$ implies a displacement of $ql_H^2$, with $l_H$ being the magnetic length. For extended states, the combined effect of a short range disorder and a rapidly oscillating wave function at high Landau levels results in an additional, potentially larger, displacement whose sign depends on the electron's energy.