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We investigate theoretically the existence at low temperature of acommensurate (4/7) crystalline phase of a layer of either He isotope on top ofa He-4 layer adsorbed on graphite. We make use of a recently developed,systematically improvable variational approach which allows us to treat bothisotopes on an equal footing. We confirm that no commensurate crystallinesecond layer of He-4 forms, in agreement with all recent calculations.Interestingly and more significantly, we find that even for He-3 there is noevidence of such a phase, as the system freezes into an {\it incommensurate}crystal at a coverage lower than that (4/7) at which a commensurate one hasbeen predicted, and for which experimental claims have been made. Implicationson the interpretation of recent experiments with helium on graphite arediscussed.

Second layer crystalline phase of helium films on graphite