Description
In this talk I will provide an overview of the search for supersolids, an elusive state of matter in which
superfluid and solid behaviors coexist. Theoretical speculations on the coexistence of off-diagonal long-range order
and crystalline order (with the accompanying shear rigidity) date from the 1960s; after a long dormant period, there
was great excitement in 2004 when several experimental groups announced the observation of nonclassical
rotational inertia, a hallmark of the putative supersolid phase, in samples of solid 4He. Alas, careful experiments from
2004-2012 determined that the signals of a supersolid phase were most likely a result of defects in the solid that
affected the shear modulus, with little to do with ODRLO. However, the experiments stimulated interest in a
hydrodynamic theory of supersolids, with the identification of new collective modes. I will review this hydrodynamic
theory, in which point defects in the solid play a starring role. While not immediately relevant to solid 4He, variants of
this work may be relevant to supersolid phases observed in dipolar atomic gases over the past five years.
