Long wavelength spatial oscillations of high frequency current noise in 1D electron systems

TL;DR

This paper theoretically investigates finite frequency current noise in a 1D electron system with a scatterer, revealing high-frequency spatial oscillations influenced by band curvature and Coulomb interactions, with implications for Luttinger liquids.

Contribution

It introduces a detailed analysis of high-frequency noise oscillations in 1D systems, incorporating effects of band curvature and Coulomb interactions within the Luttinger liquid framework.

Findings

Finite frequency noise exhibits spatial oscillations with wavelength πv_F/ω.

Band curvature causes decay and beat patterns in noise oscillations.

Coulomb interactions reduce amplitude and alter the wavelength of oscillations.

Abstract

Finite frequency current noise is studied theoretically for a 1D electron system in presence of a scatterer. In contrast to zero frequency shot noise, finite frequency noise shows spatial oscillations at high frequencies with wavelength $\pi v_F/\omega$. Band curvature leads to a decay of the amplitude of the noise oscillations as one moves away from the scatterer, superimposed by a beat. Furthermore, Coulomb interaction reduces the amplitude and modifies the wavelength of the oscillations, which we inspect in the framework of the Luttinger liquid (LL) model. The oscillatory noise contributions are only suppressed altogether when the LL interaction parameter $g \to 0$.