The challenge of the Supersolid state of matter

The supersolid is a fascinating state of matter in which the long-range
order, typical of the solid phase, coexists with some form of
superfluidity, where atoms are free to flow without any dissipation. The
first experimental evidence of supersolidity comes in 2004 in solid 4He.
The true mechanism leading to supersolidity is still unknown and there
is the diffuse believing that disorder plays a fundamental role. We
study via the Path Integral Ground State technique the properties of 2D
solid 4He. We find that perfect crystals do not display Bose-Einstein
condensation, and thus no superfluidity. Otherwise vacancies are really
efficient at inducing a condensate fraction. But vacancies are shown to
be attractive, leading to the conviction that they phase-separate out of
the solid. However, we find that when many vacancies are inserted into
the crystal, they tend to transform themselves into dislocations able to
sustain a condensate fraction in the simulated systems.