Topological nodal line in superfluid $^3$He and the Anderson theorem

TL;DR

This study demonstrates that in superfluid $^3$He, impurity scattering within certain subsystems preserves the energy gap and topological features, supporting the idea that Anderson theorem can protect unconventional superfluid states from disorder.

Contribution

The paper provides experimental evidence that impurity scattering confined within subsystems can preserve topological features in superfluid $^3$He, validating a conjecture about robustness against disorder.

Findings

Oriented columnar defects do not significantly alter the energy spectrum.

The superfluid maintains a Dirac nodal line despite strong scattering.

Subsystems obeying the Anderson theorem can protect topological states.

Abstract

Superconductivity and superfluidity with anisotropic pairing -- such as $d$-wave in cuprates and $p$-wave in superfluid $^3$He -- are strongly suppressed by impurities. Meanwhile, for applications, the robustness of Cooper pairs to disorder is highly desired. Recently, it has been suggested that unconventional systems become robust if the impurity scattering mixes quasiparticle states only within individual subsystems obeying the Anderson theorem that protects conventional superconductivity. Here, we experimentally verify this conjecture by measuring the temperature dependence of the energy gap in the polar phase of superfluid $^3$He. We show that oriented columnar non-magnetic defects do not essentially modify the energy spectrum, which has a Dirac nodal line. Although the scattering is strong, it preserves the momentum along the length of the columns and forms robust subsystems according to the conjecture. This finding may stimulate future experiments on the protection of topological superconductivity against disorder and on the nature of topological fermionic flat bands.