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

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 $g \to 0$.