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Possible quantum liquid crystal phases of helium monolayers

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 incommensurate 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.