Fractional Wigner crystal in the helical Luttinger liquid

TL;DR

This paper investigates the edge states of topological insulators with strong interactions, revealing a fractional Wigner crystal of charge e/2 that exhibits unique oscillations and spin textures.

Contribution

It introduces the concept of a fractional Wigner crystal in helical Luttinger liquids, showing novel density oscillations and spin correlations due to strong interactions.

Findings

Discovery of fractional charge e/2 Wigner crystal oscillations

Persistence of spin-momentum locking signatures

Identification of non-trivial spin textures associated with fractional order

Abstract

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they instead represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we show that the state characterized by such fractional oscillations still bears the signatures of spin momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a non trivial spin texture.