Localized Bose-Einstein condensation in disordered liquid 4He films

We present neutron scattering measurements of the phonon-roton and layer modes of liquid helium films adsorbed in 25-Å pore diameter gelsil as a function of temperature. The goal is to determine whether the well-defined phonon-roton and layer modes observed at low temperature at partial fillings of the porous media persist as well-defined modes at higher temperatures above the superfluid phase, as is the case of fully filled pores (3D liquid). We find that well defined P-R modes exist in films at temperatures well above the superfluid phase. This is the case at all fillings investigated. Liquid 4He in porous media is an example of a Bose liquid in disorder. The existence of P-R modes above Tc suggests the existence of patches or islands of Bose condensed liquid that have order [localized Bose-Einstein condensation (LBEC)] above Tc. The interpretation is that the well-defined P-R modes propagate in the patches of BEC. Gelsil partially filled with liquid helium shows the same LBEC behavior as found previously in fully filled gelsil (as in a 3D liquid).