Role of shear modulus and statistics in the supersolidity of helium

The first clear evidence for supersolidity in helium came from experiments in which the resonant period of a torsional oscillator decreased below 0.2 K, indicating that some of the solid 4 He decoupled from the oscillation. More recently, shear-modulus measurements on solid 4 He revealed an unexpected increase with the same dependence on temperature and 3 He impurities. The similarities raised the possibility that the period drop in torsion experiments is simply due to the stiffening of the solid. Here, we report the same measurements on solid 3 He, a Fermi solid instead of a Bose solid. The anomalous modulus increase found in hexagonal close-packed (hcp) 4 He, is also found in hcp 3 He. However, in the case of 3 He, the shear modulus increase is not accompanied by a corresponding period change of the torsional oscillator. We conclude that elastic stiffening alone does not produce the changes in the torsional-oscillator period and that decoupling occurs only in a stiffened Bose solid.