Minimal model for disorder-induced missing moment of inertia in solidH4e

Abstract

The absence of a missing moment inertia in clean solid $^{4}\text{H}\text{e}$ suggests that the minimal experimentally relevant model is the one in which disorder induces superfluidity in a bosonic lattice. To this end, we explore the relevance of the disordered Bose-Hubbard model in this context. We posit that a clean array of $^{4}\text{H}\text{e}$ atoms is a self-generated Mott insulator; that is, the $^{4}\text{H}\text{e}$ atoms constitute the lattice as well as the ``charge carriers.'' With this assumption, we are able to interpret the textbook defect-driven supersolids as excitations of either the lower or the upper Hubbard bands. In the experiments at hand, disorder induces the closing of the Mott gap through the generation of midgap localized states at the chemical potential. Depending on the magnitude of the disorder, we find that the destruction of the Mott state takes place for $d+z>4$ either through a Bose-glass phase (strong disorder) or through a direct transition to a superfluid (weak disorder). For $d+z<4$, disorder is always relevant. The critical value of the disorder that separates these two regimes is shown to be a function of the boson filling, interaction, and the momentum cutoff. We apply our work to the experimentally observed enhancement $^{3}\text{H}\text{e}$ impurities have on the onset temperature for the missing moment of inertia. We find quantitative agreement with experimental trends.