Wigner Crystal in One Dimension

TL;DR

This paper investigates a one-dimensional electron gas with Coulomb interactions, revealing Wigner crystal behavior at low densities, collective excitations, and implications for nonlinear transport and experimental observations in semiconductor structures.

Contribution

It demonstrates the existence of Wigner crystal correlations in 1D electron gases with long-range Coulomb interactions and connects these findings to experimental phenomena.

Findings

Charge excitation energies agree with RPA calculations.

Density correlations at 4k_F decay slowly, indicating Wigner crystal formation.

Pinning of the Wigner crystal explains nonlinear transport properties.

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.