The second-layer phase diagrams of $^4$He and $^3$He adsorbed on graphite are investigated. Intrinsically rounded specific-heat anomalies are observed at 1.4 and 0.9 K, respectively, over extended density regions in between the liquid and incommensur
ate solid phases. They are identified to anomalies associated with the Kosterlitz-Thouless-Halperin-Nelson-Young type two-dimensional melting. The prospected low temperature phase (C2 phase) is a commensurate phase or a $textit{quantum hexatic}$ phase with quasi-bond-orientational order, both containing $textit{zero}$-$textit{point}$ defectons. In either case, this would be the first atomic realization of the $textit{quantum liquid crystal}$, a new state of matter. From the large enhancement of the melting temperature over $^3$He, we propose to assign the observed anomaly of $^4$He-C2 phase at 1.4 K to the hypothetical supersolid or superhexatic transition.
A low-energy electron diffraction (LEED) apparatus which works at temperatures down to about 100 mK is designed to obtain structural information of 2D helium on graphite. This very low temperature system can be realized by reducing the thermal inflow
from the LEED optics to the sample which is cooled by cryogen-free dilution refrigerator. The atomic scattering factor of He is also estimated using a kinematical model, which suggests that the diffraction signal from He atom can well be obtained by using a delay-line detector instead of a fluorescent screen.
