Coulomb Drag in Mesoscopic Hopping Insulators

As it is known, the role of Coulomb correlations in hopping transport is still not understood in detail and different works contain controversial conclusions in this concern. In what follows, we are going to consider an effect which is completely controlled by the Coulomb correlations. Namely, we mean the Coulomb drag between two-dimensional hopping insulators. Assuming that the principal role is played by the critical resistors in both the active layer and the passive one, we have analyzed the “ratchet” mechanism of the drag. The effect consists of the modulation of an activation energy in the “passive” resistor by the non-equilibrium electric dipole formed on the “active” resistor in the presence of electric field. The dipole originates due to a hop of a single electron and has a transient character. Namely, the effect of this non-equilibrium dipole on the “passive” resistor takes place at the timescale shorter than typical relaxation times for an establishment of the equilibrium in the “passive” plane. The latter fact is of principal importance. The effect vanishes in a sample with infinite size in the plane provided that the distance between the layers is large enough. For finite-size samples, both the effect magnitude and sign depend on the sample’s size. We have analyzed the dependencies in relevant limiting cases. It is important to note that the effect drastically depends on the distance between the two planes. Thus, we hope that studies of this effect can, in particular, throw light on the role of Coulomb correlations in hopping transport. We have compared the results with those of previously published papers.