Mobility of ions trapped below a free surface of superfluid ³he

The p-wave superfluid phases of ³He-B and ³He-A are topologically nontrivial. Topological properties manifest themselves as the formation of bound states at a surface. Unusual properties of the p-wave superfluids also appear around impurities, such as an ion immersed in liquid ³He. In this article, we present the mobility of positive and negative ions trapped below a free surface of ³He-B and ³He-A measured down to 250 μK, which is much lower than the temperatures attained in previous experiments in the bulk. Mobility measurements are conducted for two purposes: one is to figure out details of the scattering of a quasiparticle by an impurity in p-wave superfluids, and the other is to detect the surface Andreev bound states (SABSs) at a free surface of ³He-B formed as a result of the nontrivial topology of ³He-B. We find, in both superfluid phases, that the mobility shows a considerable increase with decreasing temperature. In both superfluid phases, the mobility of a negative ion at high temperatures is in agreement with the theory for the bulk, in which the p-wave coherence in a Bogoliubov quasiparticle upon scattering is taken into account. This agreement demonstrates a crucial role of the p-wave coherence in scattering. The mobility at low temperatures deviates from the theory, particularly in ³He-B, and the possible origins of the deviation are discussed. The mobility of a positive ion, by contrast, does not follow the theory that includes the p-wave coherence, in both ³He-B and ³He-A. In ³He-B, the mobility of both negative and positive ions remarkably shows no dependence on the depth of the ions even if the depth is varied over the coherence length. The lack of depth dependence indicates that SABSs have little contribution to the momentum transfer rate of the ions, whichmight reflect the unusual Majorana aspect of SABSs.