Electrons embedded in liquid 3 He form mesoscopic bubbles with radii large compared to the interatomic distance between 3 He atoms, voids of N bubble ≈ 200 3 He atoms, generating a negative ion with a large effective mass that scatters thermal excitations. Electron bubbles in chiral superfluid 3 He-A also provide a local probe of the ground state. We develop scattering theory of Bogoliubov quasiparticles by negative ions embedded in 3 He-A that incorporates the broken symmetries of 3 He-A, particularly broken symmetries under time-reversal and mirror symmetry in a plane containing the chiral axisl. Multiple scattering by the ion potential, combined with branch conversion scattering by the chiral order parameter, leads to a spectrum of Weyl Fermions bound to the ion that support a mass current circulating the electron bubble -the mesoscopic realization of chiral edge currents in superfluid 3 He-A films. A consequence is that electron bubbles embedded in 3 He-A acquire angular momentum, L ≈ −(N bubble /2)hl, inherited from the chiral ground state. We extend the scattering theory to calculate the forces on a moving electron bubble, both the Stokes drag and a transverse force, F W = e c v × B W , defined by an effective magnetic field, B W ∝l, generated by the scattering of thermal quasiparticles off the spectrum of Weyl Fermions bound to the moving ion. The transverse force is responsible for the anomalous Hall effect for electron bubbles driven by an electric field reported by the RIKEN group. Our results for the scattering cross section, drag and transverse forces on moving ions are compared with experiments, and shown to provide a quantitative understanding of the temperature dependence of the mobility and anomalous Hall angle for electron bubbles in normal and superfluid 3 He-A. We also discuss our results in relation to earlier work on the theory of negative ions in superfluid 3 He.

Following the recent proposal by Weeks et al., which suggested that indium (or thallium) adatoms deposited on the surface of graphene should turn the latter into a quantum spin Hall (QSH) insulator characterized by a sizeable gap, we perform a systematic study of the transport properties of this system as a function of the density of randomly distributed adatoms. While the samples are, by construction, very disordered, we find that they exhibit an extremely stable QSH phase with no signature of the spatial inhomogeneities of the adatom configuration. We find that a simple rescaling of the spin-orbit coupling parameter allows us to account for the behaviour of the inhomogeneous system using a homogeneous model. This robustness opens the route to a much easier experimental realization of this topological insulator. We additionally find this material to be a very promising candidate for thermopower generation with a target temperature tunable from 1 to 80 K and an efficiency ZT ≈ 1.