Quantum Wire Hybridized with a Single-Level Impurity

TL;DR

This paper investigates how a single impurity affects electron transport in a one-dimensional quantum wire, revealing a divergence in the effective width of the antiresonance at low energies using renormalization group analysis.

Contribution

It introduces a theoretical analysis of impurity effects in a Luttinger liquid, showing a generalized Breit-Wigner antiresonance with diverging width at the Fermi level.

Findings

Transmission coefficient exhibits a Breit-Wigner shape with diverging width.

Local density of states shows strong low-energy modifications.

Antiresonance width diverges at the Fermi level.

Abstract

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a back-scattering of electrons in the wire which strongly affects its low energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, $\mathcal{T}(\varepsilon)$, and a local density of states, $\nu(\varepsilon)$ at low energies $\varepsilon $. In particular, we have found that the antiresonance in $\mathcal{T}(\varepsilon)$ has a generalized Breit-Wigner shape with the effective width $\Gamma(\varepsilon)$ which diverges at the Fermi level.