Mechanical properties of helium: is it a “supersolid?"

Helium’s small mass and weak interatomic forces make it a truly quantum material. At temperatures below 2.17 K, liquid ⁴He becomes a superfluid, with many unusual properties. A classic 1946 experiment by Andronikashvili measured the “superfluid fraction” - the zero viscosity part of the liquid which decoupled from a torsional oscillator.  A recent experiment observed similar decoupling for solid ⁴He below 200 mK, the signature of the “non-classical rotational inertia” which would characterize a new supersolid phase of matter. During the past 5 years, many experiments have looked at other properties of solid helium, but have not yet found definitive proof of other “super” behavior.  We have developed new techniques and measured the mechanical (flow and elastic) properties of solid helium, to look for unusual behavior at low temperatures. We see no flow, but our recent shear modulus measurements show a large and unexpected stiffening of the solid at very low temperatures, with an associated dissipation peak. These are clearly related to the decoupling seen in torsional oscillator experiments, but the exact relationship is not understood.  I describe our efforts to understand the roles of crystalline defects and quantum statistics in the behavior of this very quantum solid.