Fragility of surface states in topological superfluid $^3$He

TL;DR

This study investigates the fragility of surface states in topological superfluid $^3$He, revealing that surface magnetic scattering significantly suppresses superfluid transition temperature and alters bound states, challenging their presumed robustness.

Contribution

It demonstrates that surface Andreev bound states in topological superfluid $^3$He are fragile and sensitive to surface scattering conditions, contrary to expectations from topological protection.

Findings

Surface magnetic scattering greatly suppresses $T_c$.

Increased low-energy bound states due to magnetic scattering.

Surface states are more fragile than in topological insulators.

Abstract

Topological superfluid $^3$He, with unconventional spin-triplet p-wave pairing, provides a model system for topological superconductors, which have attracted significant interest through potential applications in topologically protected quantum computing. In topological insulators and quantum Hall systems, the surface/edge states, arising from bulk-surface correspondence and the momentum space topology of the band structure, are robust. Here we demonstrate that in topological superconductors the surface Andreev bound states, which depend on the momentum space topology of the emergent order parameter, are fragile with respect to the details of surface scattering. We confine superfluid $^3$He within a cavity of height comparable to the Cooper pair diameter. We precisely determine the superfluid transition temperature $T_{\mathrm{c}}$ and the suppression of the superfluid energy gap, for different scattering conditions tuned in situ, and compare to the predictions of quasi-classical theory. We discover that surface magnetic scattering leads to unexpectedly large suppression of $T_{\mathrm{c}}$, corresponding to an increased density of low energy bound states.