Electron bubbles and Weyl fermions in chiral superfluidHe3−A

Abstract

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.

Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors

“…Although longitudinal conductivity at temperature T ∆ mf is hardly affected by the impurity size or chiral order, the Hall conductivity depends strongly on both. When impurities are smaller than the inverse Fermi wavelength k f R 1 and impurity scattering is predominantly s-wave, the thermal Hall conductivity is severely suppressed for chiral states with ν = 2 but remains finite for ν = 5. Hall transport vanishes in the dirty limit due to the loss of chiral pairing, and bulk transport is absent in the clean limit due to the loss of impurityinduced states at ε = 0.…”

“…The A-phase of superfluid 3 He was definitively identified as a chiral p-wave superfluid by the observation of anomalous Hall transport of electrons moving through a quasiparticle fluid of chiral Fermions. 4,5 In 2D materials, chiral d-wave superconductivity is predicted for doped graphene 6,7 , while a chiral p-wave state is proposed for MoS. 8 For the 3D pnictide SrPtAs, where there is evidence from µSR of broken time-reversal symmetry onsetting at the superconducting transition, 9 a chiral d-wave state has been proposed theoretically as the ground state.…”

Models for supercritical motion in a superfluid Fermi liquid

“…[42,43] for reviews. Small objects have been extensively studied using the quantum approach, modeling the scattering of quasiparticles from the object by scattering phase shifts [44][45][46][47][48]. We are interested in the motion of the object at velocities exceeding the Landau critical velocity.…”

Superfluid helium-3 in confined quarters

“…Thus, ion studies probe excitations of pure 3 He. 20,21 The intrinsic properties of normal and the superfluid phases is rich, well studied and quantitatively understood theoretically. For these reasons superfluid 3 He has been widely thought of as unique compared to electronic superconductors in that BCS pairing occurs in essentially a pristine material free of defects and impurity disorder.…”