Coulomb blockade microscopy of spin density oscillations and fractional charge in quantum spin Hall dots

TL;DR

This paper investigates spin density oscillations and fractional charge in quantum spin Hall dots created by magnetic barriers, revealing how spin density patterns and fractionalization depend on magnetic configuration, interactions, and can be probed via chemical potential shifts.

Contribution

It demonstrates the emergence of fractional charge and spin oscillations in quantum spin Hall dots with magnetic barriers, linking these phenomena to particle number and interactions.

Findings

Half-integer charge trapped in the dot with antiparallel barriers

Spin density oscillations depend on particle number and interactions

Spatial shifts in chemical potential can probe fractional charge and spin patterns

Abstract

We evaluate the spin density oscillations arising in quantum spin Hall quantum dots created via two localized magnetic barriers. The combined presence of magnetic barriers and spin-momentum locking, the hallmark of topological insulators, leads to peculiar phenomena: a half-integer charge is trapped in the dot for antiparallel magnetization of the barriers, and oscillations appear in the in-plane spin density, which are enhanced in the presence of electron interactions. Furthermore, we show that the number of these oscillations is determined by the number of particles inside the dot, so that the presence or the absence of the fractional charge can be deduced from the in-plane spin density. We show that when the dot is coupled with a magnetized tip, the spatial shift induced in the chemical potential allows to probe these peculiar features.