Coulomb Drag between Quantum Wires

Abstract

We study Coulomb drag in a pair of parallel one-dimensional electron systems within the framework of the Tomanaga-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 trans-resistivity {\em diverges}, due to the formation of locked charge density waves. At temperature well above a cross-over temperature $T^{\ast }$ the trans-resistivity 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 $T^{\ast }$ relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The cross-over temperature $T^{\ast }$ depends sensitively on the wire width, inter-wire distance, Fermi wavelength and the effective Bohr radius. For wire distances $\bar{d}\gg k_F^{-1}$ it is exponentially suppressed with $T/E_F\sim \exp [-\bar{d}{k}_F/(1-K_{c-})]$. The behavior changes drastically if each of the two wires develop spin gaps. In this case we find that the trans-resistivity {\em vanishes} at zero temperature. We discuss our results in view of possible experimental realizations in GaAs-AlGaAs semiconductor structures.

16 pages, 3 figures, revTeX

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