Wigner Crystallization in inhomogeneous one dimensional wires

TL;DR

This paper investigates electron behavior in one-dimensional power law potentials, analyzing density profiles, Wigner crystal formation, and tunneling spectra, revealing how localization affects momentum space wavefunctions and experimental signatures.

Contribution

It provides a theoretical analysis of electron density, Wigner crystallization, and tunneling spectra in inhomogeneous 1D wires, including the momentum space wavefunction at the Fermi surface.

Findings

Density profile varies with electron density regime.

Localization causes broadening of momentum wavefunction.

Tunneling spectrum sharpens with localization.

Abstract

We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum space wavefunction of the electron at the Fermi surface, which can be measured in experiments on tunneling between parallel wires. The onset of localization leads to a dramatic broadening of the momentum space wavefunction together with pronounced sharpening (in energy) of the tunneling spectrum.