title: Fractional Wigner Crystal in the Helical Luttinger Liquid.
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 demonstrate 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 nontrivial spin texture.
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
authors.forename: N
authors.initials: N
authors.lastname: Traverso Ziani
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
authors.forename: F
authors.initials: F
authors.lastname: Crépin
authors.affiliation: Institute for Theoretical Physics and Astrophysics, University of Würzburg, 97074 Würzburg, Germany.
authors.forename: B
authors.initials: B
authors.lastname: Trauzettel