Wigner crystal physics in quantum wires

TL;DR

This paper reviews the physics of Wigner crystals in quantum wires, focusing on their spin and orbital properties in one-dimensional and quasi-one-dimensional regimes, and how electron density influences their structure and magnetic phases.

Contribution

It provides a comprehensive analysis of Wigner crystal behavior in quantum wires, including spin interactions, inhomogeneity effects, and the transition from 1D to zigzag structures with detailed phase diagrams.

Findings

Electron spins form an antiferromagnetic Heisenberg chain with small exchange coupling.

Inhomogeneity causes spin-charge separation violation affecting conductance.

Zigzag structures exhibit diverse spin polarization phases.

Abstract

The physics of interacting quantum wires has attracted a lot of attention recently. When the density of electrons in the wire is very low, the strong repulsion between electrons leads to the formation of a Wigner crystal. We review the rich spin and orbital properties of the Wigner crystal, both in the one-dimensional and quasi-one-dimensional regime. In the one-dimensional Wigner crystal the electron spins form an antiferromagnetic Heisenberg chain with exponentially small exchange coupling. In the presence of leads the resulting inhomogeneity of the electron density causes a violation of spin-charge separation. As a consequence the spin degrees of freedom affect the conductance of the wire. Upon increasing the electron density, the Wigner crystal starts deviating from the strictly one-dimensional geometry, forming a zigzag structure instead. Spin interactions in this regime are dominated by ring exchanges, and the phase diagram of the resulting zigzag spin chain has a number of unpolarized phases as well as regions of complete and partial spin polarization. Finally we address the orbital properties in the vicinity of the transition from a one-dimensional to a quasi-one-dimensional state. Due to the locking between chains in the zigzag Wigner crystal, only one gapless mode exists. Manifestations of Wigner crystal physics at weak interactions are explored by studying the fate of the additional gapped low-energy mode as a function of interaction strength.