Helical gaps in interacting Rashba wires at low electron densities

TL;DR

This paper studies how strong electron interactions in Rashba wires at low densities influence the formation of a helical gap, revealing oscillatory behavior of the gap's critical magnetic field and its impact on conductance signatures.

Contribution

It introduces a Wigner crystal approach to analyze the helical gap in strongly interacting Rashba wires, showing the gap persists but with a density-dependent critical magnetic field.

Findings

Helical gap exists even under strong interactions.

Critical magnetic field oscillates with electron density.

Conductance signatures are significantly affected.

Abstract

Rashba spin-orbit coupling and a magnetic field perpendicular to the Rashba axis have been predicted to open a partial gap ("helical gap") in the energy spectrum of noninteracting or weakly interacting one-dimensional quantum wires. By comparing kinetic energy and Coulomb energy we show that this gap opening typically occurs at low electron densities where the Coulomb energy dominates. To address this strongly correlated limit, we investigate Rashba wires using Wigner crystal theory. We find that the helical gap exists even in the limit of strong interactions but its dependence on electron density differs significantly from the weakly interacting case. In particular, we find that the critical magnetic field for opening the gap becomes an oscillatory function of electron density. This changes strongly the expected signature of the helical gap in conductance measurements.