# Second layer crystalline phase of helium films on graphite

## TL;DR

This study uses a variational approach to examine the possibility of a second layer crystalline phase of helium on graphite, finding no evidence for such a phase in either He-4 or He-3, contrary to some experimental claims.

## Contribution

It provides a systematic theoretical analysis showing the absence of a second layer commensurate crystalline phase for both helium isotopes on graphite.

## Key findings

- No second layer commensurate crystalline phase for He-4.
- He-3 forms an incommensurate crystal, not a commensurate one.
- Results align with recent calculations and challenge some experimental interpretations.

## Abstract

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 He-4 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 He-4 forms, in agreement with all recent calculations. Interestingly and more significantly, we find that even for He-3 there is no evidence 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 has been predicted, and for which experimental claims have been made. Implications on the interpretation of recent experiments with helium on graphite are discussed.