Long-wavelength spatial oscillations of high-frequency current noise in one-dimensional electron systems

Finite-frequency current noise is studied theoretically for a one-dimensional electron system in the presence of a scatterer. In contrast to zero-frequency shot noise, finite-frequency noise shows spatial oscillations at high frequencies with wavelength πv_F/ω. 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 g⃗0.