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arXiv:cond-mat/9604026

Friedel oscillations in Luttinger liquids

Reinhold Egger, Hermann Grabert

Published Apr 4, 1996• 0 citations
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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.

DOI
10.48550/arxiv.cond-mat/9604026

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We study Friedel oscillations in one-dimensional electron liquids for arbitrary electron-electron interaction and arbitrary impurity strength. Explicit results for spinless as well as spin- 12\frac{1}{2}21​ electrons are given. In the case of Luttinger-liquid leads, the Friedel oscillations decay as ${x}^{\ensuremath{-}g}$ far away from the impurity where ggg is the interaction constant. For a weak scatterer, a slower decay is found at small-to-intermediate distances from the impurity, with a crossover to the asymptotic ${x}^{\ensuremath{-}g}$ decay.
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Using a bosonization and variational Gaussian wave-functional method we analytically calculate the Friedel oscillations induced by a single impurity in one-dimensional electron systems with long-range Coulomb interaction. It is shown that the Friedel oscillations are drastically different from those in electron systems with short-range interaction. First, in the long-range case the oscillatory part of the Friedel oscillations is not periodic as that in the short-range case. Second, in the long-range case the envelope of the Friedel oscillations decays as $\mathrm{exp}[\ensuremath{-}\mathrm{const}(\mathrm{ln}{x)}^{1/2}]$ far away from the impurity, which is much slower than the power law in the short-range case.
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