Elastic anomaly of helium films at a quantum phase transition

Helium films show various quantum phases that undergo quantum phase transitions by changing coverage n. We found anomalous elastic phenomena in bosonic He4 and fermionic He3 films adsorbed on a glass substrate. The films stiffen under ac strain at low temperature with an excess dissipation. The onset temperature of the stiffening decreases to 0 K as n approaches a critical coverage nc. The elastic anomaly is explained by thermal activation of helium atoms from the localized to extended states with a distributed energy gap. We determine the energy band structure of helium films from elasticity. The ground states of He4 and He3 at n<nc, which are possibly a sort of Mott insulator or Mott glass, are identically gapped and compressible.