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Single and multi-particle scattering in Helical liquid with an impurity

We examine the scattering behavior from a single non magnetic impurity in a helical liquid. A helical liquid is a one dimensional system with a pair of counter propagating edge states, which are time reversal partners. In the absence of a magnetic field, time reversal symmetry is conserved and hence single particle scattering is prohibited. However, multi particle processes are possible. We examine the backscattering current and noise, and derive the effective scattering charge. A magnetic field enhances the backscattered current, but reduces the effective scattering charge. We find that the scattering charge can vary between $e$ and $2e$, depending on the strength of electron-electron interactions and the magnetic field.