Fig. 1: Polar phase of superfluid ³He under nanostructured confinement.

a The topology- and symmetry-protected Dirac nodal line in the spectrum of the Bogoliubov quasiparticles in the polar phase forms a circle in the p_z = 0 plane, while the superfluid energy gap is axially symmetric with respect to \(\hat{{{{{{{{\bf{z}}}}}}}}}\) axis and reaches maxima at p_z = ± p_F with p_F being the Fermi momentum. The Berry phase changes by π on a path around the nodal line, see Supplementary Note 1. b A cartoon illustrating the Anderson theorem: In systems with s-wave pairing and isotropic gap, a quasiparticle (silver ball) changes its momentum direction (blue arrows) on scattering events, but the effective gap the quasiparticle “sees” remains the same. Remarkably, similar picture applies in the p-wave polar phase if scattering preserves p_z component of momentum. c In general unconventional superconductor with anisotropic gap, the Anderson theorem is not applicable and the gap is suppressed. d The phase diagram of superfluid ³He confined in nafen-243 nanomaterial is occupied by the polar phase, while the suppression of T_c compared to the transition T_cb in bulk (not confined) ³He is relatively small. The circles are our measurements and squares are from ref. ²². Lines are fit to the model of ref. ²⁶, see the text for details. e Idealized model of the nanostructured confinement used to engineer the polar phase: A system of randomly distributed columnar defects of diameter d and spacing D, oriented along the z-axis and providing specular quasiparticle scattering, which conserves the z-component p_z of the momentum. For such model, the Anderson theorem is extended to a spin-triplet p-wave superfluid—the polar phase²⁴. f A microphotograph of the nafen-243 material used for ³He confinement in this work. For this material²² 〈d〉 ≈ 9 nm and 〈D〉 ≈ 35 nm. Unlike the perfect model in panel (e), the real material has orientational disorder of the Al₂O₃ strands, which somewhat violates the Anderson theorem and results in the small suppression of T_c in the phase diagram. This imperfection is not under good control, and the T_c suppression is different for the two sets of data in panel (d), although the two samples have the same nominal density.