Anomalous Friedel oscillations in a quasi-helical quantum dot

TL;DR

This paper explores unusual Friedel oscillations and spin patterns in a quasi-helical quantum dot influenced by spin-orbit coupling and magnetic fields, revealing novel states with potential experimental signatures.

Contribution

It develops a Luttinger liquid model for a quantum dot in a quasi-helical regime, uncovering anomalous oscillations and spin textures not previously described.

Findings

Anomalous Friedel oscillations with doubled wavelength are identified.

Distinct spin patterns emerge in the magnetization of the states.

Signatures of these states are detectable in transport measurements.

Abstract

The charge and spin patterns of a quantum dot embedded into a spin-orbit coupled quantum wire subject to a magnetic field are investigated. A Luttinger liquid theory is developed, taking into account open boundaries and finite magnetic field. In the quasi-helical regime, when spin-orbit effects dominate over the Zeeman interaction, peculiar states develop at the Fermi surface of the dot. Anomalous Friedel oscillations with twice the expected wavelength develop in the wavefunction of collective excitations of such states, accompanied by peculiar spin patterns in their magnetization. Both effects are analyzed in detail and shown possible to be probed in transport experiments. The stability against electron interactions and magnetic field is investigated. We also discuss how signatures of such states survive in the total charge and spin densities.