Coulomb drag between a metal and a Wigner crystal

We calculated the Coulomb drag contribution to the resistivity and the transresistivity for a double layer system, in which the passive layer is a Wigner crystal pinned by impurities, and the active one is a metal. We found that in quasi one dimensional systems both quantities are suppressed at low temperatures by the constraints of energy and momentum conservation in electron-phonon scattering. In two dimensions both quantities are ~T^4, which is consistent with Bloch law for the contribution of electron-phonon interaction to the resistivity. Strong impurities in the Wigner crystal decrease the transresistivity significantly when their number reaches the logarithm of the number of sites in the crystal. In contrast, the drag contribution to the resistivity is found to be independent of the impurities, at least as long as their density is kept zero in the thermodynamic limit.