Phonon-roton modes and a Bose glass phase in nanoscale liquid $^4$He

We present neutron scattering measurements of the elementary phonon-roton modes of liquid $^4$He confined in nanoporous media. The aim is to compare phonon-roton (P-R) and superfluid density measurements in helium at nanoscales and in disorder. A specific goal is to determine the region of temperature and pressure in which well defined phonon-roton modes (and therefore BEC) exist and compare this with the superfluid region. In 25 $\AA$ mean pore diameter gelsil Yamamoto et al.[1] find that the superfluid phase extends up to a temperature T$_c$ = 1.4 K at saturated vapor pressure (SVP) (p $\simeq$ 0) and up to a pressure p$_c$ = 34 bar at (T $\simeq$ 0). There is apparently a Quantum Phase Transition at p$_c$ = 34 bar[1]. We find well defined P-R modes (BEC) extend above T$_c$ at SVP (up to T$_\lambda$ = 2.17 K) and to pressures above p$_c$ (up to a pressure p = 36.3-36.8 bars at T $\simeq$ 0 but no modes above this pressure). This suggests that there is a Bose glass phase consisting of local regions of BEC (fragmented BEC) separated by regions with no BEC surrounding the superfluid phase at all p and T. We compare this phase diagram with other dirty Bose systems. [1] Yamamoto et al. Phys. Rev. Lett. 93, 075302 (2004).