Fractional charge oscillations in quantum spin Hall quantum dots

TL;DR

This paper investigates how two-particle backscattering induces fractional charge oscillations in quantum dots at the edges of topological insulators, revealing the influence of magnetization and interactions on charge and spin density patterns.

Contribution

It demonstrates the role of correlated backscattering in fractional charge oscillations and explores the interplay with Jackiw-Rebbi charge fractionalization in topological insulator quantum dots.

Findings

Fractional charge oscillations depend on magnetization angle.

Two-particle backscattering affects spin density oscillations.

Charge and spin density oscillations have different wavelengths.

Abstract

We show that correlated two-particle backscattering can induce fractional charge oscillations in a quantum dot built at the edge of a two-dimensional topological insulator by means of magnetic barriers. The result nicely complements recent works where the fractional oscillations were obtained employing of semiclassical treatments. Moreover, since by rotating the magnetization of the barriers a fractional charge can be trapped in the dot via the Jackiw-Rebbi mechanism, the system we analyze offers the opportunity to study the interplay between this noninteracting charge fractionalization and the fractionalization due to two-particle backscattering. In this context, we demonstrate that the number of fractional oscillations of the charge density depends on the magnetization angle. Finally, we address the renormalization induced by two-particle backscattering on the spin density, which is characterized by a dominant oscillation, sensitive to the Jackiw-Rebbi charge, with a wavelength twice as large as the charge density oscillations.