Nonclassical rotational inertia for a supersolid under rotation

As proposed by Leggett [4], the supersolidity of a crystal is characterized by the Non Classical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau and Rica [5], we prove that NCRI occurs. This is done by analyzing the ground state of the aforementioned model, which is related to a sphere packing problem, and then deriving a theoretical formula for the inertia momentum. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.