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 4He and fermionic 3He 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 for the first time the energy band structure of helium films from elasticity. The ground states of 4He and 3He at n < n_c are identically gapped and compressible, which are possibly a sort of Mott insulator or Mott glass.