Wigner crystal in one dimension

Abstract

A one-dimensional gas of electrons interacting with long-range Coulomb forces [V(r)\ensuremath{\approxeq}1/r] is investigated. The excitation spectrum consists of separate collective charge and spin modes. For arbitrarily weak Coulomb repulsion density correlations at wave vector 4${\mathit{k}}_{\mathit{F}}$ decay extremely slowly and are best described as those of a one-dimensional Wigner crystal. Pinning of the Wigner crystal then leads to the nonlinear transport properties characteristic of charge density waves. The results allow a consistent interpretation of the plasmon and spin excitations observed in one-dimensional semiconductor structures, and suggest an interpretation of some of the observed features in terms of ``spinons.''