Influence of the contacts on the conductance of interacting quantum wires

We investigate how the conductance G through a clean interacting quantum wire is affected by the presence of contacts and noninteracting leads. The contacts are defined by a vanishing two-particle interaction to the left and a finite repulsive interaction to the right or vice versa. No additional single-particle scattering terms (impurities) are added. We first use Bosonization and the local Luttinger liquid picture and show that within this approach G is determined by the properties of the leads regardless of the details of the spatial variation of the Luttinger liquid parameters. This generalizes earlier results obtained for steplike variations. In particular, no single-particle backscattering is generated at the contacts. We then study a microscopic model applying the functional renormalization group and show that the spatial variation of the interaction produces single-particle backscattering, which in turn leads to a reduced conductance. We investigate how the smoothness of the contacts affects G and show that for decreasing energy scale its deviation from the unitary limit follows a power law with the same exponent as obtained for a system with a weak single-particle impurity placed in the contact region of the interacting wire and the leads.