Spin-orbit coupling in quasi-one-dimensional Wigner crystals

TL;DR

This paper investigates how Rashba spin-orbit coupling influences the charge and spin properties of quasi-one-dimensional Wigner crystals, revealing spectrum gaps and altered spin interactions.

Contribution

It introduces a new understanding of SOC effects in quasi-1D Wigner crystals, including spectrum gaps and a novel spin Hamiltonian for strong SOC regimes.

Findings

Partial spectral gap opens at certain electron density ratios with weak SOC.

Charge spectrum deviates from linearity at small wave vectors due to SOC.

Strong SOC leads to triplet-dominant ground states and a new spin Hamiltonian.

Abstract

We study the effect of Rashba spin-orbit coupling (SOC) on the charge and spin degrees of freedom of a quasi-one-dimensional (quasi-1D) Wigner crystal. As electrons in a quasi-1D Wigner crystal can move in the transverse direction, SOC cannot be gauged away in contrast to the pure 1D case. We show that for weak SOC, a partial gap in the spectrum opens at certain ratios between density of electrons and the inverse Rashba length. We present how the low-energy branch of charge degrees of freedom deviates due to SOC from its usual linear dependence at small wave vectors. In the case of strong SOC, we show that spin sector of a Wigner crystal cannot be described by an isotropic antiferromagnetic Heisenberg Hamiltonian any more, and that instead the ground state of neighboring electrons is mostly a triplet state. We present a new spin sector Hamiltonian and discuss the spectrum of Wigner crystal in this limit.