Continuum theory of superflow in supersolid 4He:: A review

The recent observation of non-classical rotational inertia in solid He-4 for temperatures T < 200 mK, and the continued non-observation of unusual flow associated with "zeropoint defectons", favors the Leggett picture of Non-Classical Rotational Inertia over the Andreev-Lifshitz zero-point defecton picture of possible superflow in this system. We discuss the nature of the wave function, the Leggett one-body phase function upper bound for the superfluid fraction, and more complex forms for the phase-function and how this affects the net momentum density of this many-body system. The general properties of quantum vortices in such a system are briefly discussed.