Minimal Model for Disorder-induced Missing Moment of Inertia in Solid $^4$He
Abstract
The absence of a missing moment inertia in clean solid He suggests that the minimal experimentally relevant model is 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 He atoms is a self-generated Mott insulator, that is, the He 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 upper Hubbard bands. In the experiments at hand, disorder induces a closing of the Mott gap through the generation of mid-gap 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 either through a Bose glass phase (strong disorder) or through a direct transition to a superfluid (weak disorder). For , 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 cut off. We apply our work to the experimentally observed enhancement He impurities has on the onset temperature for the missing moment of inertia. We find quantitative agreement with experimental trends.
Cite
@article{arxiv.cond-mat/0612505,
title = {Minimal Model for Disorder-induced Missing Moment of Inertia in Solid $^4$He},
author = {Jiansheng Wu and Philip Phillips},
journal= {arXiv preprint arXiv:cond-mat/0612505},
year = {2015}
}
Comments
9 pages, 5 figures: Extended version of previous paper in which the pase diagram for the disordered Bose-Hubbard model is computed using mean-field theory and one-loop RG. The criterion for the Bose glass is derived explicitly. (a few typos are corrected)