Friedel oscillations in Luttinger liquids

Abstract

We study the density disturbance of a correlated 1D electron liquid in the presence of a scatterer or a barrier. The 2k_F-periodic density profile away from the barrier (Friedel oscillation) is computed for arbitrary electron--electron interaction and arbitrary impurity strength. We find that in presence of correlations, the Friedel oscillation decays slower than predicted by Fermi liquid theory. In the case of a spinless Luttinger liquid characterized by an interaction constant g<1, the asymptotic decay of the Friedel oscillation is x^-g. For a weak scatterer, the decay is even slower at small-to-intermediate distances from the impurity, with a crossover to the asymptotic x^-g law.