%0 Journal Article %T Charge and spin density in the helical Luttinger liquid %A N. Traverso Ziani %A C. Fleckenstein %A F. Cr¨¦pin %A B. Trauzettel %J Physics %D 2015 %I arXiv %X 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. %U http://arxiv.org/abs/1511.03157v1