Observation of a Superfluid Component within Solid Helium

We demonstrate by neutron scattering that a localized superfluid component exists at high pressures within solid helium in aerogel. Its existence is deduced from the observation of two sharp phonon-roton spectra which are clearly distinguishable from modes in bulk superfluid helium. These roton excitations exhibit different roton gap parameters than the roton observed in the bulk fluid at freezing pressure. One of the roton modes disappears after annealing the samples. Comparison with theoretical calculations suggests that the model that reproduces the observed data best is that of superfluid double layers within the solid and at the helium-substrate interface.

Figure 1

Intensity maps of inelastic and elastic neutron scattering data taken on the time-of-flight spectrometer IN6 at ILL [23] at a temperature of 50 mK at three pressures. The color-scale has been normalized to the elastic scattering intensity of the aerogel. The diffraction and small angle scattering from the aerogel appear in pink-black along the zero energy transfer line, $E=0\mathrm{meV}$, as the Bragg-peaks of solid helium polycrystals for $Q>1.9{\AA }^{-1}$. No scattering from amorphous solid helium was detected. The Bragg peaks are attributed tentatively to hcp and bcc bulk structures, marked by white and yellow circles, respectively. An average crystallite diameter of 50 nm is obtained for all structures from the diffraction peaks [14]. For comparison we also show the dispersion relation of bulk liquid helium at $T=0.5\mathrm{K}$ and 20 bar (upper blue lines) [20]. The lower blue lines represent rotonlike intensities already known from helium films on aerogel [6] that can be identified as a “layer roton.” Phonons emerging from the bulk helium Bragg peaks within the measured $Q$ range were not detected [9]. The signal with highest intensity around $E=1.2\mathrm{meV}$, $Q=2.1{\AA }^{-1}$ is proportional to the amount of solid helium [14].

Figure 2

Intensity cuts along $Q=2.09{\AA }^{-1}$, taken from Figs. 1a, 1b, 1c. Also shown is the effect of annealing from Fig. 3a. The gray lines mark the intensity maxima.

Figure 3

The effect of annealing at $\sim 1.3\mathrm{K}$ and 53.8 bar. The spectrum in pane (a) has been taken at 600 mK after heating the sample from 50 mK to 1.3 K, followed by recooling back to 600 mK. The upper dispersion line, which we identify with excitations in superfluid double layers, has vanished. We identify the remaining lower roton with an excitation that is propagating in superfluid double layers at the aerogel–solid-helium interface. Pane (b) is generated by subtracting the intensities of Fig. 3a from those of Fig. 1c, selecting the upper roton excitation which has vanished by annealing. The dark streaks in Fig. 3b around zero energy come from a slight shift of the Bragg peaks during annealing [14].

Figure 4

The figure shows the measured roton dispersion relation $E(Q)$ in the confined phases for the three pressures given in Fig. 1. The curves represent results of fits to the $Q$-sliced intensity maps of Fig. 1a, 1b, 1c. Examples of the slices I (energy) are shown in Fig. 2. The energy of the roton minimum $E_{\Delta }$ and wave number $Q_{\Delta }$ in the bulk liquid is also shown (magenta line) as a function of pressure. It follows a line that is clearly distinct from the roton minimum of the two localized phases, which are nearly independent of pressure. Only a slight shift of its $E_{\Delta }$ of only $4.7\mu \mathrm{eV}/10\mathrm{bar}$ is noticed as opposed to $\approx 49\mu \mathrm{eV}/10\mathrm{bar}$ in the bulk phase. Also the $E_{\Delta }$, of the lower roton, whose energy is much lower than the roton gap in the bulk liquid, is, within statistics, independent of pressure.

Figure 5

Dependence of the roton parameters $E_{\Delta }$ and $Q_{\Delta }$ on pressure in various geometries. The measured values are represented by the two heavy red bars; see Fig. 4. The light blue lines in the grey shaded area show a family of double-layer configurations where the solid substrate has been modeled by a 3–9 potential of well depth between 4 and 30 K. The red curve shows theoretical results for a 2D model, which agree quite well with results for an atomic monolayer (blue curve). We also show $E_{\Delta }$ and $Q_{\Delta }$ of bulk liquid helium [20] as a function of pressure up to the melting line (magenta line). The horizontal dotted line shows the limiting energy of the bulk roton at melting pressure at 0.62 meV.