Charge and spin density in helical Luttinger liquids (Vol. 47 No. 3)

Planar spin helix, pinned by an impurity

Often an electron confined to one spatial dimension does not have many options. It can have spin up or down and it can go right or left. In helical systems the possibilities are further reduced: the spin projection is tied to the direction of motion. This phenomenon is called spin-momentum locking and takes place at the edges of two-dimensional topological insulators. Its consequences are exciting for spintronics: since spin up and down electrons counter-propagate, spin transport can be easily generated by charge currents. In our work, we identify peculiar properties of the weakly interacting helical Luttinger liquid. We address the interesting question: Are the charge density and spin correlations influenced by spin-momentum locking? While for strong interactions the system becomes a Wigner crystal of fractional charges e/2 built on a strongly anisotropic spin wave (which we have shown in a previous publication), in this work, we demonstrate that, for weak interactions, density correlations are featureless, i.e. the density is not affected by impurities. However, spin correlations are well represented by a planar spin helix that can be pinned by magnetic impurities.

N. Traverso Ziani, C. Fleckenstein, F. Crépin and B. Trauzettel, Charge and spin density in the helical Luttinger liquid, EPL 113, 37002 (2016)