Second-layer crystalline phase of helium films on graphite

We investigate theoretically the existence at low temperature of a commensurate (4/7) crystalline phase of a layer of either He isotope on top of a He4 layer adsorbed on graphite. We make use of a recently developed, systematically improvable variational approach which allows us to treat both isotopes on an equal footing. We confirm that no commensurate crystalline second layer of He4 forms, in agreement with all recent calculations. Interestingly and more significantly, we find that even for He3 there is no evidence of such a phase, as the system freezes into an incommensurate crystal at a coverage lower than that (4/7) at which a commensurate one has been predicted and for which experimental claims have been made. Implications for the interpretation of recent experiments with helium on graphite are discussed.