Accompanying data for "Fragility of surface states in topological superfluid 3He"

The article detailing the findings of this study, and the used methods and techniques, has been published in Nature Communications 12, 1574 (2021). https://doi.org/10.1038/s41467-021-21831-y

'expr_Tc_suppression_[boundary condition].dat' files list the measured values of superfluid transition temperature both in the confined cavity and in the bulk markers corresponding to different boundary conditions and various pressures, i.e. various values of effective cavity height. These values are included in Figures 2a,b and 3a in the manuscript.

'expr_gap_[boundary condition]_[pressure].dat' files give the measured temperature dependence of the spatially averaged energy gap of superfluid A phase of helium-3 corresponding to two boundary conditions and various pressures. Values of the gap are based on the measured NMR frequency shift in the superfluid state as described in Supplementary Note 1 in the manuscript. Two pressures are included in Figure 2c in the article. All four pressures in specular case are shown in Supplementary Figure 8 and all four pressures in diffuse case in Supplementary Figure 9.

'initial_slopes_[boundary condition].dat' give the measured initial slopes of the superfluid frequency shift versus temperature determined within 10% range below the measured superfluid transition temperature in the cavity for two boundary conditions and various pressures. These values are needed in conversion between the frequency shift and the energy gap and are plotted in Supplementary Figure 4 in the manuscript.

'calc_Tc_suppression_S[specularity].dat' show the calculated suppressed superfluid transition temperature as a function of effective cavity height for various different specularities.

'calc_gap_S[specularity]_D[effective height].dat' give the calculated spatially averaged values of the energy gap of superfluid 3He-A as a function of temperature, corresponding to different surface specularities and effective heights of the cavity. The effective heights for specularity S = 0.10 correspond to mean heights of the cavity at four pressures used in the experiments, determined by the limits set by the uncertainty in the height measurement and by the small pressurre-dependent height distortion. The diffuse S = 0.00 calculations exactly match these values or are off by insignificant amount.

In all the calculations we have used the quasiclassical weak-coupling approach, as described in the Supplementary Note 3 of the manuscript. In gap calculations also the trivial pressure-dependent strong-coupling scaling has been included, as detailed in Supplementary Note 4.

Values of bulk (or fully specular) superfluid transition temperature are given by D. S. Greywall in Phys. Rev. B 33, 7520 (1986) (https://doi.org/10.1103/PhysRevB.33.7520). These values are used to convert the unitless gap calculations into real units.

Values of the weak-coupling bulk energy gap of 3He-A can be found, for example, by using E. V. Thuneberg's calculator from http://ltl.tkk.fi/research/theory/qc/bcsgap.html. The values as a function of temperature are also given in file 'calc_gap_bulk.dat'.