Coulomb drag between quantum wires

Abstract

We study Coulomb drag in a pair of parallel one-dimensional electron systems within the framework of the Tomonaga-Luttinger model. We find that Coulomb coupling has a much stronger effect on one-dimensional wires than on two-dimensional layers: At zero temperature the transresistivity diverges, due to the formation of locked charge density waves. At temperature well above a crossover temperature $T^{*}$ the transresistivity follows a power law $\rho \propto T^x,$ where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter $K_{c-}$ of the relative charge mode. At temperature below $T^{*}$ relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The crossover temperature $T^{*}$ depends sensitively on the wire width, interwire distance, Fermi wavelength and the effective Bohr radius. For wire distances $\overline{d}\gg k_F^{-1}$ it is exponentially suppressed with $T^{*}{/E}_F\sim \exp [-\overline{d}{k}_F/(1\mathrm{}-K_{c-}\left)\right].$ The behavior changes drastically if each of the two wires develop spin gaps. In this case we find that the transresistivity vanishes at zero temperature. We discuss our results in view of possible experimental realizations in $\mathrm{GaAs}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ semiconductor structures.