We show that the five
α cluster states recently observed in
20Ne,
slightly above the five
α threshold energy, are Bose-Einstein
condensates of five
α clusters. The states are described well using a
superfluid cluster model, where the order parameter is defined. We suggest that
the the five
α states are fragmented. Theory predicts the emergence of a
five
α rotational roton band characterized by a large moment of inertia.
This band is formed through roton excitations of the five
α BEC vacuum
and possesses dual properties of superfluidity and crystallinity, a property of
supersolidity. The persistent existence of such a roton bandis discussed and
confirmed for the four
α condensate above the four
α threshold in
16O and the three
α condensate above the three
α threshold
in
12C.