We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $ u=1$ or fractional $ u=1/3$ quantum Hall bar. We show that in the limit of a large capacitive cou
pling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $ u=1/3$ fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $ u=1$ and $ u=1/3$.
A spin-orbit coupled quantum wire, with one end proximate to an s-wave superconductor, can become a topological superconductor, with a Majorana mode localized at each end of the superconducting region. It was recently shown that coupling one end of s
uch a topological superconductor to $two$ normal channels of interacting electrons leads to a novel type of frustration and a quantum critical point when both channels couple with equal strength. We propose an experimental method to access this critical point in a $single$ quantum wire and show its resilience to disorder.
Low-temperature electrical conductance spectroscopy measurements of quantum point contacts implemented in p-type GaAs/AlGaAs heterostructures are used to study the Zeeman splitting of 1D subbands for both in-plane and out-of-plane magnetic field orie
ntations. The resulting in-plane g-factors agree qualitatively with those of previous experiments on quantum wires while the quantitative differences can be understood in terms of the enhanced quasi-1D confinement anisotropy. The influence of confinement potential on the anisotropy is discussed and an estimate for the out-of-plane g-factor is obtained which, in contrast to previous experiments, is closer to the theoretical prediction.
