Chiral superfluid helium-3 in the quasi-two-dimensional limit

Anisotropic pair breaking close to surfaces favors the chiral A phase of the superfluid $^3$He over the time-reversal invariant B phase. Confining the superfluid $^3$He into a cavity of height $D$ of the order of the Cooper pair size characterized by the coherence length $\xi_0$ - ranging between 16 nm (34 bar) and 77 nm (0 bar) - extends the surface effects over the whole sample volume, thus allowing stabilization of the A phase at pressures $P$ and temperatures $T$ where otherwise the B phase would be stable. In this Letter, the surfaces of such a confined sample are covered with a superfluid $^4$He film to create specular quasiparticle scattering boundary conditions, preventing the suppression of the superfluid order parameter. We show that the chiral A phase is the stable superfluid phase under strong confinement over the full $P$-$T$ phase diagram down to a quasi-two-dimensional limit $D / \xi_0 = 1$ , where $D = 80$ nm. The planar phase, which is degenerate with the chiral A phase in the weak-coupling limit, is not observed. The gap inferred from measurements over the wide pressure range from 0.2 to 21.0 bar leads to an empirical ansatz for temperature-dependent strong-coupling effects. We discuss how these results pave the way for the realization of the fully gapped two-dimensional $p_x + ip_y$ superfluid under more extreme confinement.