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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.

The transport properties of a CNT capacitively coupled to a molecule vibrating along one of its librational modes are studied and its transport properties analyzed in the presence of an STM tip. We evaluate the linear charge and thermal conductances of the system and its thermopower. They are dominated by position-dependent Franck-Condon factors, governed by a position-dependent effective coupling constant peaked at the molecule position. Both conductance and thermopower allow to extract some information on the position of the molecule along the CNT. Crucially, however, thermopower sheds also light on the vibrational levelspacing, allowing to obtain a more complete characterization of the molecule even in the linear regime.

We study the spin ordering of a quantum dot defined via magnetic barriers in an interacting quantum spin Hall edge. The spin-resolved density-density correlation functions are computed. We show that strong electron interactions induce a ground state with a highly correlated spin pattern. The crossover from the liquid-type correlations at weak interactions to the ground state spin texture found at strong interactions parallels the formation of a one-dimensional Wigner molecule in an ordinary strongly interacting quantum dot., Comment: Accepted for publication on Physica Status Solidi - Rapid Research Letters (early view)

We consider a quantum spin Hall system in a two-terminal setup, with an extended tunneling contact connecting upper and lower edges. We analyze the effects of this geometry on the backscattering current as a function of voltage, temperature, and strength of the electron interactions. We find that this configuration may be useful to confirm the helical nature of the edge states and to extract their propagation velocity. By comparing with the usual quantum point contact geometry, we observe that the power-law behaviors predicted for the backscattering current and the linear conductance are recovered for low enough energies, while different power-laws also emerge at higher energies., Comment: 8 pages, 6 figures, published version