Fractional charge oscillations in quantum dots with quantum spin Hall effect

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 those fractional oscillations were predicted in the strong-coupling regime. 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. We demonstrate that the number of fractional oscillations of the charge density depends on the magnetization angle. In fact, a rotating magnetization can add or subtract fractional charges from the dot continuously. Finally, we address the renormalization induced by two-particle backscattering on the spin density, which is characterized by a dominant oscillation with a length twice as large as the charge-density oscillations.