Charge and spin density in the helical Luttinger liquid

TL;DR

This paper investigates the unique charge and spin density behaviors in the weakly interacting helical Luttinger liquid, revealing unconventional correlation functions and impurity effects due to spin-momentum locking.

Contribution

It uncovers the absence of Friedel and Wigner oscillations in density correlations and the formation of a planar spin wave, highlighting the effects of magnetic impurities.

Findings

Density-density correlations lack Friedel and Wigner oscillations.

Spin-spin correlations form a planar spin wave.

Magnetic impurities can pin the spin density wave.

Abstract

The weakly interacting helical Luttinger liquid, due to spin momentum locking, is characterized by extremely peculiar local observables: we show that the density-density correlation functions do not exhibit signatures of Friedel and Wigner oscillations, and that spin-spin correlation functions, which are strongly anisotropic, witness the formation of a planar spin wave. Moreover, we demonstrate that the most relevant scattering potentials involving a localized impurity are not able to modify the electron density, while only magnetic impurities can pin the planar spin density wave.