Excited-State Wigner Crystals in One Dimension

TL;DR

This paper introduces a method to identify excited-state Wigner crystals in a one-dimensional electron gas, revealing incommensurate structures with unique electronic properties that are lower in energy than the uniform Fermi fluid.

Contribution

It presents a novel symmetry-broken mean-field approach to systematically construct and analyze excited-state Wigner crystals in one dimension.

Findings

ESWCs are incommensurate and lower in energy than the Fermi fluid

Some ESWCs exhibit asymmetrical band gaps leading to anisotropic conductivity

ESWCs display unusual electronic structural characteristics

Abstract

Wigner crystals (WC) are electronic phases peculiar to low-density systems, particularly in the uniform electron gas. Since its introduction in the early twentieth century, this model has remained essential to many aspects of electronic structure theory and condensed-matter physics. Although the (lowest-energy) ground-state WC (GSWC) has been thoroughly studied, the properties of excited-state WCs (ESWCs) are basically unknown. To bridge this gap, we present a well-defined procedure to obtain an entire family of ESWCs in a one-dimensional electron gas using a symmetry-broken mean-field approach. While the GSWC is a commensurate crystal (i.e.~the number of density maxima equals the number of electrons), these ESWCs are incommensurate crystals exhibiting more or less maxima. Interestingly, they are lower in energy than the (uniform) Fermi fluid state. For some of these ESWCs we have found asymmetrical band gaps, which would lead to anisotropic conductivity. These properties are associated to unusual characteristics in their electronic structure.