Electron bubbles and Weyl fermions in chiral superfluid He 3 -A

Electrons embedded in liquid He3 form mesoscopic bubbles with large radii compared to the interatomic distance between He3 atoms, voids of Nbubble≈200 He3 atoms, generating a negative ion with a large effective mass that scatters thermal excitations. Electron bubbles in chiral superfluid He3-A also provide a local probe of the ground state. We develop a scattering theory of Bogoliubov quasiparticles by negative ions embedded in He3-A that incorporates the broken symmetries of He3-A, particularly broken symmetries under time reversal and mirror symmetry in a plane containing the chiral axis l. 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 - a mesoscopic realization of chiral edge currents in superfluid He3-A films. A consequence is that electron bubbles embedded in He3-A acquire angular momentum, L≈-(Nbubble/2)l, 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, FW=ecv×BW, defined by an effective magnetic field, BWl, 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 He3-A. We also discuss our results in relation to earlier work on the theory of negative ions in superfluid He3.