Nonclassical Rotational Inertia of a Supersolid

As proposed by Leggett [Phys. Rev. Lett. 25, 1543 (1970)10.1103/PhysRevLett.25.1543], the supersolidity of a crystal is characterized by the nonclassicalical Rotational Inertia (NCRI) property. Using a model of quantum crystal introduced by Josserand, Pomeau, and Rica [Phys. Rev. Lett. 72, 2426 (1994)10.1103/PhysRevLett.72.2426], 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 moment of inertia. We infer a lower estimate for the NCRI fraction, which is a landmark of supersolidity.