Coulomb drag at the onset of Anderson insulators

Abstract

I study the Coulomb drag between two identical layers in the Anderson insulating state. The dependence of the transresistance ${\ensuremath{\rho}}_{t}$ on the localization length \ensuremath{\xi} is considered, for both a Mott insulator and an Efros-Shklovskii (ES) insulator. In the former, ${\ensuremath{\rho}}_{t}$ is monotonically increasing with \ensuremath{\xi}; in the latter, the presence of a Coulomb gap leads to an opposite result: ${\ensuremath{\rho}}_{t}$ is enhanced with a decreasing \ensuremath{\xi}, with the same exponential factor as the single layer resistivity. This distinction reflects the relatively pronounced role of excited density fluctuations in the ES state, implied by the enhancement in the rate of hopping processes at low frequencies. The magnitude of drag is estimated for typical experimental parameters in the different cases. It is concluded that a measurement of drag can be used to distinguish between the interacting and noninteracting insulating state.