Wigner Crystal in One Dimension

Abstract

A one--dimensional gas of electrons interacting with long--range Coulomb forces ($V(r) \approx 1/r$) is investigated. The excitation spectrum consists of separate collective charge and spin modes, with the charge excitation energies in agreement with RPA calculations. For arbitrarily weak Coulomb repulsion density correlations at wavevector $4k_F$ 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 CDW. 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''. A possible explanation for nonlinear transport phenomena is given.