Z_{4} parafermions in Weakly Interacting Superconducting Constrictions at the Helical Edge of Quantum Spin Hall Insulators.

Parafermions are generalizations of Majorana fermions that may appear in interacting topological systems. They are known to be powerful building blocks of topological quantum computers. Existing proposals for realizations of parafermions typically rely on strong electronic correlations which are hard to achieve in the laboratory. We identify a novel physical system in which parafermions generically develop. It is based on a quantum constriction formed by the helical edge states of a quantum spin Hall insulator in the vicinity of an ordinary s-wave superconductor. Interestingly, our analysis suggests that Z_{4} parafermions are emerging bound states in this setup in the weakly interacting regime. Furthermore, we identify a situation in which Majorana fermions and parafermions can coexist.

Current noise as a probe for Wigner molecules.

The effects of a Wigner molecule on the current noise and conductance of a one-dimensional quantum dot with two electrons are investigated. Focusing on a lateral transport setup, the sequential regime is considered. Tunnelling rates through the dot are evaluated within an exact diagonalisation scheme. They strongly depend on electron interactions, showing a markedly different behaviour in the presence of a Wigner molecule with respect to the weak interactions case, and thus modify the transport and current noise and the dot. For weak interactions negative differential conductance and super-Poissonian noise are found. As interactions increase, a Wigner molecule develops: it suppresses the negative differential conductance and turns the shot noise to sub-Poissonian values. In particular, the noise is found to be a sensitive probe of the Wigner molecule.

Thermally enhanced Wigner oscillations in two-electron 1D quantum dots.

Motivated by a recent experiment (Pecker et al 2013 Nat. Phys. 9 576), we study the stability, with respect to thermal effects, of Friedel and Wigner density fluctuations for two electrons trapped in a one-dimensional quantum dot. Diagonalizing the system exactly, the finite-temperature average electron density is computed. While the weak and strong interaction regimes display a Friedel oscillation or a Wigner molecule state at zero temperature, which as expected smear and melt as the temperature increases, a peculiar thermal enhancement of Wigner correlations in the intermediate interaction regime is found. We demonstrate that this effect is due to the presence of two different characteristic temperature scales: T(F), dictating the smearing of Friedel oscillations, and T(W), smoothing Wigner oscillations. In the early Wigner molecule regime, for intermediate interactions, T(F) < T(W) leading to the enhancement of the visibility of Wigner oscillations. These results complement those obtained within the Luttinger liquid picture, valid for larger numbers of particles.