Helical nuclear spin order in a strip of stripes in the Quantum Hall regime

TL;DR

This paper explores how hyperfine interactions in a quantum Hall system modeled as coupled quantum wires can induce a helical nuclear spin order, with electron-electron interactions significantly raising the transition temperature and providing experimental signatures.

Contribution

It demonstrates the formation of a helical nuclear spin order in a quantum Hall regime modeled by coupled wires, highlighting the role of electron-electron interactions in enhancing transition temperatures.

Findings

Nuclear spins form a helix due to hyperfine interactions.

Electron-electron interactions increase transition temperatures.

Resistivity signatures indicate nuclear spin order presence.

Abstract

We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin order, for instance for the resistivity of the system at transitions between different quantum Hall plateaus.