On the Supersolid State of Matter

TL;DR

This paper establishes a theoretical condition for supersolidity, linking it to zero-point vacancies, and critically examines experimental claims of supersolidity in helium, proposing alternative explanations.

Contribution

It provides a rigorous proof that supersolidity requires zero-point vacancies and challenges previous experimental interpretations of supersolid behavior.

Findings

Superfluidity in solids requires zero-point vacancies.

Commensurate solids breaking continuous translation symmetry cannot be superfluid.

Alternative explanation for Kim and Chan's experiment involves helium interfaces.

Abstract

We prove that the necessary condition for a solid to be also a superfluid is to have zero-point vacancies, or interstitial atoms, or both, as an integral part of the ground state. As a consequence, superfluidity is not possible in commensurate solids which break continuous translation symmetry. We discuss recent experiment by Kim and Chan [Nature, {\bf 427}, 225 (2004)] in the context of this theorem, question its bulk supersolid interpretation, and offer an alternative explanation in terms of superfluid helium interfaces.