Tuning pair-breaking at the surface of topological superfluid $^3$He

Since the discovery of superconductivity in heavy fermion metals and oxide materials many emerging superconducting materials have been found to exhibit unconventional, non s-wave, pairing. In contrast to s-wave superconductors, they are extremely sensitive to scattering by non-magnetic defects and surfaces. Topological superfluid $^3$He, with unconventional p-wave pairing, provides a model system to understand the influence of surface scattering of quasiparticle excitations in the absence of defect and impurity scattering, which is of relevance to future mesoscopic device applications of topological superconductors. Here we confine superfluid $^3$He within a cavity of height comparable to the Cooper pair diameter. We precisely determine the effect of surface scattering on both the superfluid transition temperature $T_{\mathrm{c}}$ and the suppression of the superfluid energy gap. We demonstrate that the surface scattering can be tuned in situ by adjustment of the isotopic composition of the helium surface boundary layer. In particular we show that suppression of superfluidity is eliminated by a surface coating of thin superfluid $^4$He film, opening the way to studies of superfluid $^3$He in the quasi-2D limit. On the other hand, with a magnetic surface boundary layer of solid $^3$He, an unexpectedly large suppression of $T_{\mathrm{c}}$ is observed, which we model by exchange scattering.