Registered state and a two-dimensional Bose liquid of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>in mesopores of hectorite

In two-dimensional (2D) mesopores of hectorite that have an open spacing of 17--20 \AA{} between framework layers supported by pillars, the adsorption and motional state of $^{4}\mathrm{He}$ adatoms were studied by iso- steric heat of adsorption and heat capacity. These measurements were done by changing the amount of $^{4}\mathrm{He}$ adatoms, since the mesopores have quite a large adsorption area of 592\ifmmode\pm\else\textpm\fi{}2 ${\mathrm{m}}^{2}$/g. The results suggest that the adatoms are localized at hexagonal registered sites on the framework layers up to a coverage of 0.4 layer. At coverages exceeding 1.33\ifmmode\pm\else\textpm\fi{}0.03 layers, the isotope effect on the heat capacity and the torsional oscillator result indicates superfluidity of the $^{4}\mathrm{He}$ adatoms. The heat capacity of the superfluid is quadratic in T at low temperatures and becomes exponential above around 0.2 or 0.3 K. The dependencies are compared with the 2D phonon and roton heat capacities of the model calculations for 2D Bose particles. The comparison shows the effective hard-core diameter of the adatoms to be 4--6 \AA{}, and indicates that the correlation among the atoms is much stronger in the 2D adsorbed superfluid than in bulk superfluid where the hard core is believed to be 2.56 \AA{}. At full adsorption, there was reduction of the superfluid transition ${\mathit{T}}_{\mathit{c}}$ from the \ensuremath{\lambda} temperature, which was believed to be the effect of the size of the mesopores on the coherence length.

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