Fig. 2: Suppression of superfluid transition temperature and superfluid gap for different surface scattering conditions.

a Measured pressure dependence of T_c for close to diffuse (squares) and close to specular (circles) boundary conditions. Full lines show predicted T_c for diffuse (green) and fully specular (black) boundaries, dashed lines are best fits yielding S = 0.1 and S = 0.98. b Suppression of T_c relative to bulk superfluid transition temperature T_c0 for ‘diffuse’ boundary steeply increases with confinement. Suppression of T_c for ‘specular’ boundary is essentially eliminated. The uncertainties in temperature determination and the modelled distortion of cavity height by pressure are used to define the vertical and horizontal error bars, respectively (‘Methods’). c Spatial average of energy gap Δ_A(z), where z is the vertical position in the cavity, inferred from measured frequency shift (Supplementary Note 1), for ‘diffuse’ (squares) and ‘specular’ (circles) boundary conditions. All theoretical curves include strong-coupling corrections valid near T_c. The ‘diffuse’ experiments agree best with theory for S = 0.1 (dashed lines, see also Supplementary Fig. 9). The emergent discrepancy between theory and experiment at lower temperatures at 5.5 bar, for both scattering conditions, is in agreement with the expected temperature dependence of strong-coupling corrections to the gap (Supplementary Note 4). The width of the theoretical curves for S = 0.1 accounts for errors associated with the weak pressure dependence and uncertainty of cavity height (‘Methods’). The theoretical curves for diffuse boundary condition (solid green lines) correspond to the mean value of D/ξ₀ at given pressure, and the theoretical curves for specular boundary condition (solid orange lines) correspond to the bulk energy gaps of ³He-A. d The calculated gap profile at zero pressure for specularities between 0 and 1 in intervals of 0.1.